Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1104 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722638 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721073 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11721071 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11721068 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#88436 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10595449 | — | 3 | 1 | no | maximal |
| 9 | #10595444 | — | 3 | 1 | no | maximal |
| 10 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | #88748 | — | 2 | 1 | no | — |
| 12 | D4×#272 | — | 2 | 3 | no | — |
| 13 | #88740 | C22 | 1 | 3 | yes | complemented |
| 14 | C2×C4⋊#272 | C22 | 1 | 3 | yes | complemented |
| 15 | #88722 | — | 2 | 1 | no | — |
| 16 | D4×(C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 17 | #3828⋊C3 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×C4⋊((C3⋊D3)⋊C3) | C22 | 1 | 3 | yes | complemented |
| 19 | #3748⋊C3 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×(C3⋊(C3⋊C8))⋊C3 | C22 | 1 | 3 | yes | complemented |
| 21 | #88439 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #88438 | C22 | 1 | 3 | yes | complemented |
| 23 | #88437 | C22 | 1 | 3 | yes | complemented |
| 24 | #88436 | C22 | 1 | 3 | yes | complemented |
| 25 | #88436 | C22 | 1 | 6 | yes | complemented |
| 26 | #64366 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#1009 | — | 3 | 1 | no | — |
| 28 | C3×#1009 | — | 3 | 1 | no | — |
| 29 | C3×#1009 | — | 3 | 1 | no | — |
| 30 | C3×#1009 | — | 6 | 1 | no | — |
| 31 | #64157 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C3×#948 | — | 3 | 1 | no | — |
| 33 | #63830 | — | 3 | 3 | no | — |
| 34 | #63829 | — | 3 | 3 | no | — |
| 35 | #63825 | — | 3 | 3 | no | — |
| 36 | C2×#3714 | — | 3 | 3 | no | — |
| 37 | #63823 | — | 3 | 3 | no | — |
| 38 | #63823 | — | 3 | 3 | no | — |
| 39 | #63822 | — | 3 | 3 | no | — |
| 40 | C2×#3713 | — | 3 | 3 | no | — |
| 41 | C22×#272 | — | 2 | 3 | no | — |
| 42 | C22×(C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 43 | Q8×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 44 | D4×H(3,𝔽3) | D4 | 1 | 3 | yes | — |
| 45 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 46 | #6235 | — | 2 | 3 | no | — |
| 47 | C4⋊#272 | — | 2 | 3 | no | — |
| 48 | C4⋊#272 | C23 | 1 | 3 | yes | — |
| 49 | C4×#272 | — | 2 | 3 | no | — |
| 50 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 51 | #638⋊C3 | — | 2 | 3 | no | — |
| 52 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 3 | no | — |
| 53 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 3 | yes | — |
| 54 | C4×(C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 55 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 56 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 57 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 3 | yes | — |
| 58 | #5835 | — | 9 | 1 | no | — |
| 59 | #5835 | — | 9 | 1 | no | — |
| 60 | #5752 | — | 9 | 1 | no | — |
| 61 | C32×#41 | — | 2 | 1 | no | — |
| 62 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 63 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | #3832 | — | 2 | 1 | no | — |
| 65 | D4×C3⋊D3 | — | 2 | 3 | no | — |
| 66 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 67 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 3 | yes | complemented |
| 68 | C3×#239 | — | 6 | 2 | no | — |
| 69 | C3×#239 | — | 6 | 1 | no | — |
| 70 | C3×#239 | — | 6 | 1 | no | — |
| 71 | C3×#239 | — | 6 | 1 | no | — |
| 72 | C3×D3×D4 | — | 6 | 6 | no | — |
| 73 | C3×D3×D4 | — | 6 | 3 | no | — |
| 74 | C3×D3×D4 | — | 6 | 3 | no | — |
| 75 | C3×D3×D4 | — | 6 | 3 | no | — |
| 76 | C3×#235 | — | 3 | 3 | no | — |
| 77 | C3×#235 | — | 3 | 3 | no | — |
| 78 | C3×#235 | — | 3 | 3 | no | — |
| 79 | C3×#235 | — | 6 | 3 | no | — |
| 80 | C2×C3×D12 | — | 3 | 3 | no | — |
| 81 | C2×C3×D12 | — | 3 | 3 | no | — |
| 82 | C2×C3×D12 | — | 3 | 3 | no | — |
| 83 | C2×C3×D12 | — | 6 | 3 | no | — |
| 84 | #3748 | C2×D3 | 1 | 3 | yes | complemented |
| 85 | C2×C3⋊(C3⋊C8) | C2×D3 | 1 | 3 | yes | complemented |
| 86 | C3×#208 | — | 3 | 3 | no | — |
| 87 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 88 | #3719 | — | 3 | 1 | no | — |
| 89 | #3718 | — | 3 | 1 | no | — |
| 90 | #3717 | — | 3 | 3 | no | — |
| 91 | #3716 | — | 3 | 3 | no | — |
| 92 | #3715 | — | 3 | 3 | no | — |
| 93 | #3715 | — | 3 | 3 | no | — |
| 94 | #3714 | — | 3 | 3 | no | — |
| 95 | #3714 | — | 3 | 6 | no | — |
| 96 | #3713 | — | 3 | 3 | no | — |
| 97 | #3713 | — | 3 | 6 | no | — |
| 98 | C22×H(3,𝔽3) | C2×D4 | 1 | 3 | yes | — |
| 99 | C2×#272 | — | 2 | 3 | no | — |
| 100 | C2×#272 | — | 8 | 3 | no | — |
| 101 | C2×(C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 102 | C2×(C3⋊D3)⋊C3 | — | 8 | 3 | no | — |
| 103 | C4×H(3,𝔽3) | C2×D4 | 1 | 3 | yes | — |
| 104 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 105 | #1084 | — | 2 | 1 | no | — |
| 106 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 107 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 108 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 109 | #1009 | — | 3 | 1 | no | — |
| 110 | #1009 | — | 3 | 1 | no | — |
| 111 | #1009 | — | 3 | 1 | no | — |
| 112 | #1009 | — | 6 | 1 | no | — |
| 113 | #1009 | — | 9 | 1 | no | — |
| 114 | C3×#131 | — | 9 | 1 | no | — |
| 115 | #950 | — | 9 | 3 | no | — |
| 116 | #950 | — | 9 | 3 | no | — |
| 117 | #949 | — | 9 | 3 | no | — |
| 118 | #949 | — | 9 | 3 | no | — |
| 119 | #948 | — | 3 | 1 | no | — |
| 120 | #948 | — | 9 | 1 | no | — |
| 121 | #932 | — | 9 | 3 | no | — |
| 122 | #932 | — | 9 | 3 | no | — |
| 123 | C2×#213 | — | 9 | 3 | no | — |
| 124 | C2×#213 | — | 9 | 3 | no | — |
| 125 | #908 | — | 9 | 3 | no | — |
| 126 | #908 | — | 9 | 3 | no | — |
| 127 | #904 | — | 9 | 3 | no | — |
| 128 | C2×D24 | — | 9 | 3 | no | — |
| 129 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 130 | C22×C3×D3 | — | 6 | 6 | no | — |
| 131 | C22×C3×D3 | — | 6 | 3 | no | — |
| 132 | C22×C3×D3 | — | 6 | 3 | no | — |
| 133 | C22×C3×D3 | — | 6 | 3 | no | — |
| 134 | C32×Q8 | — | 2 | 1 | no | — |
| 135 | C32×Q8 | D12 | 1 | 1 | yes | characteristic |
| 136 | C32×Q8 | #67 | 1 | 1 | yes | characteristic |
| 137 | C32×D4 | — | 2 | 3 | no | — |
| 138 | C32×D4 | D12 | 1 | 3 | yes | — |
| 139 | C32×D4 | #67 | 1 | 3 | yes | — |
| 140 | C2×C32×C4 | — | 2 | 3 | no | — |
| 141 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 142 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 143 | #638 | — | 2 | 3 | no | — |
| 144 | C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 145 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 146 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 147 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C3×#67 | — | 6 | 6 | no | — |
| 149 | C3×#67 | — | 6 | 3 | no | — |
| 150 | C3×#67 | — | 6 | 3 | no | — |
| 151 | C3×#67 | — | 6 | 3 | no | — |
| 152 | C3×D12 | — | 3 | 3 | no | — |
| 153 | C3×D12 | — | 3 | 3 | no | — |
| 154 | C3×D12 | — | 3 | 3 | no | — |
| 155 | C3×D12 | — | 6 | 3 | no | — |
| 156 | C3×D12 | — | 6 | 6 | no | — |
| 157 | C3×D12 | — | 6 | 3 | no | — |
| 158 | C3×D12 | — | 6 | 3 | no | — |
| 159 | C3×D12 | — | 6 | 3 | no | — |
| 160 | C3×C4×D3 | — | 6 | 6 | no | — |
| 161 | C3×C4×D3 | — | 6 | 3 | no | — |
| 162 | C3×C4×D3 | — | 6 | 3 | no | — |
| 163 | C3×C4×D3 | — | 6 | 3 | no | — |
| 164 | C3×Dic6 | — | 3 | 1 | no | — |
| 165 | C3×Dic6 | — | 3 | 1 | no | — |
| 166 | C3×Dic6 | — | 3 | 1 | no | — |
| 167 | C3×Dic6 | — | 6 | 1 | no | — |
| 168 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 169 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | — |
| 170 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 171 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 172 | #576 | — | 27 | 1 | no | Sylow |
| 173 | C2×H(3,𝔽3) | — | 2 | 3 | no | — |
| 174 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 175 | #272 | — | 4 | 3 | no | — |
| 176 | (C3⋊D3)⋊C3 | — | 4 | 3 | no | — |
| 177 | C3×#41 | — | 3 | 1 | no | — |
| 178 | C3×#41 | — | 3 | 1 | no | — |
| 179 | C3×#41 | — | 6 | 1 | no | — |
| 180 | C3×#41 | — | 9 | 3 | no | — |
| 181 | C3×#41 | — | 9 | 3 | no | — |
| 182 | C3×#41 | — | 18 | 1 | no | — |
| 183 | C3×#41 | — | 18 | 1 | no | — |
| 184 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 185 | C2×C3×D4 | — | 9 | 3 | no | — |
| 186 | C2×C3×D4 | — | 9 | 3 | no | — |
| 187 | C2×C3×D4 | — | 18 | 3 | no | — |
| 188 | C2×C3×D4 | — | 18 | 3 | no | — |
| 189 | #239 | — | 6 | 1 | no | — |
| 190 | #239 | — | 6 | 1 | no | — |
| 191 | #239 | — | 6 | 2 | no | — |
| 192 | #239 | — | 6 | 1 | no | — |
| 193 | #239 | — | 18 | 1 | no | — |
| 194 | D3×D4 | — | 6 | 3 | no | — |
| 195 | D3×D4 | — | 6 | 3 | no | — |
| 196 | D3×D4 | — | 6 | 6 | no | — |
| 197 | D3×D4 | — | 6 | 3 | no | — |
| 198 | D3×D4 | — | 18 | 3 | no | — |
| 199 | #235 | — | 3 | 3 | no | — |
| 200 | #235 | — | 3 | 3 | no | — |
| 201 | #235 | — | 3 | 3 | no | — |
| 202 | #235 | — | 6 | 3 | no | — |
| 203 | #235 | — | 9 | 3 | no | — |
| 204 | C2×D12 | — | 3 | 3 | no | — |
| 205 | C2×D12 | — | 3 | 3 | no | — |
| 206 | C2×D12 | — | 3 | 3 | no | — |
| 207 | C2×D12 | — | 6 | 3 | no | — |
| 208 | C2×D12 | — | 9 | 3 | no | — |
| 209 | C3×M16 | — | 9 | 3 | no | — |
| 210 | C2×C3×C8 | — | 9 | 3 | no | — |
| 211 | #216 | — | 9 | 1 | no | — |
| 212 | #216 | — | 9 | 1 | no | — |
| 213 | #215 | — | 9 | 3 | no | — |
| 214 | #215 | — | 9 | 3 | no | — |
| 215 | #214 | — | 9 | 3 | no | — |
| 216 | #214 | — | 9 | 3 | no | — |
| 217 | #213 | — | 9 | 3 | no | — |
| 218 | #213 | — | 9 | 6 | no | — |
| 219 | #213 | — | 9 | 3 | no | — |
| 220 | #213 | — | 9 | 6 | no | — |
| 221 | #208 | — | 3 | 3 | no | — |
| 222 | #208 | — | 9 | 3 | no | — |
| 223 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 224 | C2×C3⋊C8 | — | 9 | 3 | no | — |
| 225 | Dic12 | — | 9 | 1 | no | — |
| 226 | D24 | — | 9 | 3 | no | — |
| 227 | D24 | — | 9 | 6 | no | — |
| 228 | #204 | — | 9 | 3 | no | — |
| 229 | #204 | — | 9 | 3 | no | — |
| 230 | C22×C32 | — | 2 | 3 | no | — |
| 231 | C22×C32 | C2×D12 | 1 | 3 | yes | — |
| 232 | C22×C32 | C2×#67 | 1 | 3 | yes | — |
| 233 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 234 | C2×C3⋊D3 | — | 8 | 3 | no | — |
| 235 | C2×C3×D3 | — | 6 | 6 | no | — |
| 236 | C2×C3×D3 | — | 6 | 3 | no | — |
| 237 | C2×C3×D3 | — | 6 | 3 | no | — |
| 238 | C2×C3×D3 | — | 6 | 3 | no | — |
| 239 | C2×C3×D3 | — | 24 | 3 | no | — |
| 240 | C2×C3×D3 | — | 24 | 3 | no | — |
| 241 | C2×C3×D3 | — | 24 | 3 | no | — |
| 242 | C2×C3×D3 | — | 24 | 6 | no | — |
| 243 | C32×C4 | — | 2 | 1 | no | — |
| 244 | C32×C4 | — | 2 | 3 | no | — |
| 245 | C32×C4 | C2×D12 | 1 | 3 | yes | — |
| 246 | C32×C4 | C2×#67 | 1 | 3 | yes | — |
| 247 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 248 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 249 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 250 | C3×Dic3 | — | 6 | 2 | no | — |
| 251 | C3×Dic3 | — | 6 | 1 | no | — |
| 252 | C3×Dic3 | — | 6 | 1 | no | — |
| 253 | C3×Dic3 | — | 6 | 1 | no | — |
| 254 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 255 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 256 | AGL(1,ℤ/8) | — | 27 | 3 | no | — |
| 257 | AGL(1,ℤ/8) | — | 27 | 3 | no | — |
| 258 | #135 | — | 27 | 3 | no | — |
| 259 | C2×D8 | — | 27 | 3 | no | — |
| 260 | #131 | — | 9 | 1 | no | — |
| 261 | H(3,𝔽3) | #576 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C23×C3 | — | 18 | 3 | no | — |
| 263 | C23×C3 | — | 18 | 3 | no | — |
| 264 | C22×D3 | — | 6 | 3 | no | — |
| 265 | C22×D3 | — | 6 | 3 | no | — |
| 266 | C22×D3 | — | 6 | 6 | no | — |
| 267 | C22×D3 | — | 6 | 3 | no | — |
| 268 | C22×D3 | — | 18 | 3 | no | — |
| 269 | C3×Q8 | — | 3 | 1 | no | — |
| 270 | C3×Q8 | — | 3 | 1 | no | — |
| 271 | C3×Q8 | — | 6 | 1 | no | — |
| 272 | C3×Q8 | — | 9 | 1 | no | — |
| 273 | C3×Q8 | — | 9 | 1 | no | — |
| 274 | C3×Q8 | #626 | 1 | 1 | yes | characteristic |
| 275 | C3×D4 | — | 3 | 3 | no | — |
| 276 | C3×D4 | — | 3 | 3 | no | — |
| 277 | C3×D4 | — | 6 | 3 | no | — |
| 278 | C3×D4 | — | 9 | 3 | no | — |
| 279 | C3×D4 | — | 9 | 3 | no | — |
| 280 | C3×D4 | — | 18 | 3 | no | — |
| 281 | C3×D4 | — | 18 | 3 | no | — |
| 282 | C3×D4 | — | 18 | 3 | no | — |
| 283 | C3×D4 | — | 18 | 3 | no | — |
| 284 | C3×D4 | #626 | 1 | 3 | yes | — |
| 285 | C2×C3×C4 | — | 3 | 3 | no | — |
| 286 | C2×C3×C4 | — | 3 | 3 | no | — |
| 287 | C2×C3×C4 | — | 6 | 3 | no | — |
| 288 | C2×C3×C4 | — | 18 | 3 | no | — |
| 289 | C2×C3×C4 | — | 18 | 3 | no | — |
| 290 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 291 | #67 | — | 6 | 3 | no | — |
| 292 | #67 | — | 6 | 3 | no | — |
| 293 | #67 | — | 6 | 6 | no | — |
| 294 | #67 | — | 6 | 3 | no | — |
| 295 | #67 | — | 18 | 3 | no | — |
| 296 | D12 | — | 3 | 3 | no | — |
| 297 | D12 | — | 3 | 3 | no | — |
| 298 | D12 | — | 3 | 3 | no | — |
| 299 | D12 | — | 6 | 3 | no | — |
| 300 | D12 | — | 6 | 3 | no | — |
| 301 | D12 | — | 6 | 3 | no | — |
| 302 | D12 | — | 6 | 6 | no | — |
| 303 | D12 | — | 6 | 3 | no | — |
| 304 | D12 | — | 9 | 3 | no | — |
| 305 | D12 | — | 18 | 3 | no | — |
| 306 | C4×D3 | — | 6 | 3 | no | — |
| 307 | C4×D3 | — | 6 | 3 | no | — |
| 308 | C4×D3 | — | 6 | 6 | no | — |
| 309 | C4×D3 | — | 6 | 3 | no | — |
| 310 | C4×D3 | — | 18 | 3 | no | — |
| 311 | Dic6 | — | 3 | 1 | no | — |
| 312 | Dic6 | — | 3 | 1 | no | — |
| 313 | Dic6 | — | 3 | 1 | no | — |
| 314 | Dic6 | — | 6 | 1 | no | — |
| 315 | Dic6 | — | 9 | 1 | no | — |
| 316 | C3×C8 | — | 9 | 3 | no | — |
| 317 | C3×C8 | — | 9 | 1 | no | — |
| 318 | C3⋊C8 | — | 3 | 1 | no | — |
| 319 | C3⋊C8 | — | 3 | 3 | no | — |
| 320 | C3⋊C8 | — | 9 | 1 | no | — |
| 321 | C3⋊C8 | — | 9 | 3 | no | — |
| 322 | C2×C32 | — | 2 | 3 | no | — |
| 323 | C2×C32 | — | 2 | 3 | no | — |
| 324 | C2×C32 | — | 2 | 1 | no | — |
| 325 | C2×C32 | — | 4 | 3 | no | — |
| 326 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 327 | C2×C32 | C22×#67 | 1 | 1 | yes | characteristic |
| 328 | C3⋊D3 | — | 4 | 3 | no | — |
| 329 | C3×D3 | — | 12 | 6 | no | — |
| 330 | C3×D3 | — | 12 | 3 | no | — |
| 331 | C3×D3 | — | 12 | 3 | no | — |
| 332 | C3×D3 | — | 12 | 3 | no | — |
| 333 | #41 | — | 9 | 3 | no | — |
| 334 | #41 | — | 9 | 3 | no | — |
| 335 | #41 | — | 18 | 1 | no | — |
| 336 | #41 | — | 18 | 1 | no | — |
| 337 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 338 | C2×D4 | — | 9 | 3 | no | — |
| 339 | C2×D4 | — | 9 | 3 | no | — |
| 340 | C2×D4 | — | 18 | 3 | no | — |
| 341 | C2×D4 | — | 18 | 3 | no | — |
| 342 | Q16 | — | 27 | 1 | no | — |
| 343 | SD16 | — | 27 | 3 | no | — |
| 344 | SD16 | — | 27 | 3 | no | — |
| 345 | D8 | — | 27 | 3 | no | — |
| 346 | D8 | — | 27 | 6 | no | — |
| 347 | M16 | — | 9 | 3 | no | — |
| 348 | C2×C8 | — | 9 | 3 | no | — |
| 349 | C22×C3 | — | 3 | 3 | no | — |
| 350 | C22×C3 | — | 3 | 3 | no | — |
| 351 | C22×C3 | — | 6 | 3 | no | — |
| 352 | C22×C3 | — | 18 | 3 | no | — |
| 353 | C22×C3 | — | 18 | 3 | no | — |
| 354 | C22×C3 | — | 72 | 3 | no | — |
| 355 | C22×C3 | — | 72 | 3 | no | — |
| 356 | C22×C3 | C2×#626 | 1 | 3 | yes | — |
| 357 | C2×D3 | — | 6 | 3 | no | — |
| 358 | C2×D3 | — | 6 | 3 | no | — |
| 359 | C2×D3 | — | 6 | 6 | no | — |
| 360 | C2×D3 | — | 6 | 3 | no | — |
| 361 | C2×D3 | — | 18 | 3 | no | — |
| 362 | C2×D3 | — | 24 | 3 | no | — |
| 363 | C2×D3 | — | 24 | 3 | no | — |
| 364 | C2×D3 | — | 24 | 3 | no | — |
| 365 | C2×D3 | — | 24 | 6 | no | — |
| 366 | C2×D3 | — | 72 | 3 | no | — |
| 367 | C3×C4 | — | 3 | 1 | no | — |
| 368 | C3×C4 | — | 3 | 1 | no | — |
| 369 | C3×C4 | — | 3 | 3 | no | — |
| 370 | C3×C4 | — | 3 | 3 | no | — |
| 371 | C3×C4 | — | 6 | 1 | no | — |
| 372 | C3×C4 | — | 6 | 3 | no | — |
| 373 | C3×C4 | — | 18 | 1 | no | — |
| 374 | C3×C4 | — | 18 | 1 | no | — |
| 375 | C3×C4 | C2×#626 | 1 | 3 | yes | — |
| 376 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 377 | Dic3 | — | 6 | 1 | no | — |
| 378 | Dic3 | — | 6 | 1 | no | — |
| 379 | Dic3 | — | 6 | 2 | no | — |
| 380 | Dic3 | — | 6 | 1 | no | — |
| 381 | Dic3 | — | 18 | 1 | no | — |
| 382 | C32 | — | 2 | 1 | no | — |
| 383 | C32 | #5752 | 1 | 1 | yes | characteristic, complemented |
| 384 | C32 | #5835 | 1 | 1 | yes | characteristic, complemented |
| 385 | C23 | — | 18 | 3 | no | — |
| 386 | C23 | — | 18 | 3 | no | — |
| 387 | Q8 | — | 9 | 1 | no | — |
| 388 | Q8 | — | 9 | 1 | no | — |
| 389 | Q8 | #6200 | 1 | 1 | yes | characteristic |
| 390 | D4 | — | 9 | 3 | no | — |
| 391 | D4 | — | 9 | 3 | no | — |
| 392 | D4 | — | 18 | 3 | no | — |
| 393 | D4 | — | 18 | 3 | no | — |
| 394 | D4 | — | 18 | 3 | no | — |
| 395 | D4 | — | 18 | 3 | no | — |
| 396 | D4 | #6200 | 1 | 3 | yes | — |
| 397 | C2×C4 | — | 18 | 3 | no | — |
| 398 | C2×C4 | — | 18 | 3 | no | — |
| 399 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 400 | C8 | — | 9 | 1 | no | — |
| 401 | C8 | — | 9 | 3 | no | — |
| 402 | C2×C3 | — | 2 | 3 | no | — |
| 403 | C2×C3 | — | 3 | 1 | no | — |
| 404 | C2×C3 | — | 3 | 1 | no | — |
| 405 | C2×C3 | — | 6 | 3 | no | — |
| 406 | C2×C3 | — | 6 | 3 | no | — |
| 407 | C2×C3 | — | 6 | 1 | no | — |
| 408 | C2×C3 | — | 12 | 3 | no | — |
| 409 | C2×C3 | — | 36 | 3 | no | — |
| 410 | C2×C3 | — | 36 | 3 | no | — |
| 411 | C2×C3 | C22×#626 | 1 | 1 | yes | characteristic |
| 412 | D3 | — | 12 | 3 | no | — |
| 413 | D3 | — | 12 | 3 | no | — |
| 414 | D3 | — | 12 | 6 | no | — |
| 415 | D3 | — | 12 | 3 | no | — |
| 416 | D3 | — | 36 | 3 | no | — |
| 417 | C22 | — | 18 | 3 | no | — |
| 418 | C22 | — | 18 | 3 | no | — |
| 419 | C22 | — | 72 | 3 | no | — |
| 420 | C22 | — | 72 | 3 | no | — |
| 421 | C22 | C2×#6200 | 1 | 3 | yes | — |
| 422 | C4 | — | 18 | 1 | no | — |
| 423 | C4 | — | 18 | 1 | no | — |
| 424 | C4 | C2×#6200 | 1 | 3 | yes | — |
| 425 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 426 | C3 | — | 3 | 1 | no | — |
| 427 | C3 | — | 3 | 1 | no | — |
| 428 | C3 | — | 6 | 1 | no | — |
| 429 | C3 | #10595449 | 1 | 1 | yes | characteristic |
| 430 | C2 | — | 2 | 3 | no | — |
| 431 | C2 | — | 36 | 3 | no | — |
| 432 | C2 | — | 36 | 3 | no | — |
| 433 | C2 | C22×#6200 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722675 | C2 | semidirect |
| 2. #11722638 | C2 | semidirect |
| 3. #11721689 | C2 | semidirect |
| 4. #11721073 | C2 | semidirect |
| 5. #11721071 | C2 | semidirect |
| 6. #11721068 | C2 | semidirect |
| 7. C2×#88436 | C2 | semidirect |
| 13. #88740 | C22 | semidirect |
| 14. C2×C4⋊#272 | C22 | semidirect |
| 17. #3828⋊C3 | C22 | semidirect |
| 18. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 19. #3748⋊C3 | C22 | semidirect |
| 20. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 21. #88439 | C22 | semidirect |
| 22. #88438 | C22 | semidirect |
| 23. #88437 | C22 | semidirect |
| 24. #88436 | C22 | semidirect |
| 25. #88436 | C22 | semidirect |
| 26. #64366 | D3 | semidirect |
| 31. #64157 | D3 | semidirect |
| 66. #3828 | C2×D3 | semidirect |
| 67. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 84. #3748 | C2×D3 | semidirect |
| 85. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 261. H(3,𝔽3) | #576 | semidirect |
| 383. C32 | #5752 | semidirect |
| 384. C32 | #5835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722675 | 2 |
| #11722638 | 2 |
| #11721689 | 2 |
| #11721073 | 2 |
| #11721071 | 2 |
| #11721068 | 2 |
| C2×#88436 | 2 |
| #10595449 | 3 |
| #10595444 | 3 |