Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2999 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 2999 conjugacy classes of subgroups — too many to draw. Only its 545 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 | C2×#88748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722627 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11722521 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11722519 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #11722517 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11722493 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11722491 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10596688 | — | 3 | 2 | no | maximal |
| 9 | C2×Q8×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #88748 | C22 | 1 | 4 | yes | complemented |
| 11 | #88748 | C22 | 1 | 4 | yes | complemented |
| 12 | C2×C4⋊#272 | C22 | 1 | 3 | yes | complemented |
| 13 | C2×C4×#272 | C22 | 1 | 3 | yes | complemented |
| 14 | #88722 | C22 | 1 | 8 | yes | complemented |
| 15 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 8 | yes | complemented |
| 16 | #3828⋊C3 | C22 | 1 | 12 | yes | complemented |
| 17 | #88677 | C22 | 1 | 12 | yes | complemented |
| 18 | #88672 | C22 | 1 | 4 | yes | complemented |
| 19 | #88655 | C22 | 1 | 6 | yes | complemented |
| 20 | #88654 | C22 | 1 | 24 | yes | complemented |
| 21 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 12 | yes | complemented |
| 22 | #88652 | C22 | 1 | 24 | yes | complemented |
| 23 | #88651 | C22 | 1 | 6 | yes | complemented |
| 24 | #88650 | C22 | 1 | 12 | yes | complemented |
| 25 | #88649 | C22 | 1 | 12 | yes | complemented |
| 26 | #64364 | D3 | 1 | 2 | yes | complemented |
| 27 | C3×#1007 | — | 3 | 2 | no | — |
| 28 | C2×C3×#239 | — | 3 | 2 | no | — |
| 29 | C2×C3×#239 | — | 6 | 1 | no | — |
| 30 | #64320 | — | 3 | 8 | no | — |
| 31 | #64319 | — | 3 | 8 | no | — |
| 32 | D3×#239 | — | 3 | 8 | no | — |
| 33 | #64315 | — | 3 | 8 | no | — |
| 34 | #64307 | — | 3 | 12 | no | — |
| 35 | D3×#235 | — | 3 | 12 | no | — |
| 36 | C22×#272 | C23 | 1 | 3 | yes | — |
| 37 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 12 | yes | — |
| 38 | Q8×H(3,𝔽3) | C23 | 1 | 4 | yes | — |
| 39 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 40 | C2×#1084 | C23 | 1 | 1 | yes | characteristic |
| 41 | C4⋊#272 | C23 | 1 | 12 | yes | — |
| 42 | C4×#272 | C23 | 1 | 6 | yes | — |
| 43 | C4×#272 | C23 | 1 | 6 | yes | — |
| 44 | #638⋊C3 | C23 | 1 | 8 | yes | — |
| 45 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 12 | yes | — |
| 46 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 24 | yes | — |
| 47 | #634⋊C3 | C23 | 1 | 12 | yes | — |
| 48 | #6200 | C23 | 1 | 24 | yes | — |
| 49 | #6199 | C23 | 1 | 12 | yes | — |
| 50 | #6198 | C23 | 1 | 4 | yes | — |
| 51 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 8 | yes | — |
| 52 | #6196 | C23 | 1 | 4 | yes | — |
| 53 | #5968 | — | 9 | 2 | no | — |
| 54 | #5964 | — | 9 | 1 | no | — |
| 55 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 56 | C2×C32×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 57 | #3832 | C2×D3 | 1 | 8 | yes | complemented |
| 58 | Q8×C3⋊D3 | C2×D3 | 1 | 8 | yes | complemented |
| 59 | #3828 | C2×D3 | 1 | 12 | yes | complemented |
| 60 | C3×#239 | — | 3 | 8 | no | — |
| 61 | C3×#239 | — | 3 | 8 | no | — |
| 62 | C3×#239 | — | 3 | 8 | no | — |
| 63 | C3×#239 | — | 6 | 4 | no | — |
| 64 | C3×#239 | — | 6 | 4 | no | — |
| 65 | C3×D3×Q8 | — | 3 | 8 | no | — |
| 66 | C3×#235 | — | 3 | 12 | no | — |
| 67 | C2×C3×D12 | — | 3 | 6 | no | — |
| 68 | C2×C3×D12 | — | 6 | 3 | no | — |
| 69 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 70 | C2×C3×C4×D3 | — | 6 | 3 | no | — |
| 71 | D3×#67 | — | 3 | 24 | no | — |
| 72 | #3804 | — | 3 | 8 | no | — |
| 73 | #3802 | — | 3 | 24 | no | — |
| 74 | D3×D12 | — | 3 | 12 | no | — |
| 75 | D3×D12 | — | 3 | 24 | no | — |
| 76 | C4×D32 | — | 3 | 24 | no | — |
| 77 | #3799 | — | 3 | 12 | no | — |
| 78 | #3798 | — | 3 | 24 | no | — |
| 79 | #3796 | — | 3 | 24 | no | — |
| 80 | #3795 | — | 3 | 12 | no | — |
| 81 | #3795 | — | 3 | 24 | no | — |
| 82 | D3×Dic6 | — | 3 | 12 | no | — |
| 83 | C22×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 84 | C2×#272 | — | 4 | 3 | no | — |
| 85 | C2×#272 | C24 | 1 | 6 | yes | — |
| 86 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 8 | yes | — |
| 87 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 12 | no | — |
| 88 | C4×H(3,𝔽3) | C24 | 1 | 6 | yes | — |
| 89 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 90 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 91 | (C3⋊Dic3)⋊C3 | C24 | 1 | 8 | yes | — |
| 92 | C3×2−1+4 | — | 9 | 2 | no | — |
| 93 | C2×C3×#41 | — | 9 | 1 | no | — |
| 94 | #1010 | — | 9 | 4 | no | — |
| 95 | #1009 | — | 9 | 12 | no | — |
| 96 | #1009 | — | 9 | 4 | no | — |
| 97 | #1009 | — | 9 | 8 | no | — |
| 98 | D3×#41 | — | 9 | 12 | no | — |
| 99 | D3×#41 | — | 9 | 8 | no | — |
| 100 | D3×#41 | — | 9 | 8 | no | — |
| 101 | #1007 | — | 3 | 2 | no | — |
| 102 | #1007 | — | 9 | 2 | no | — |
| 103 | #1007 | — | 9 | 8 | no | — |
| 104 | C2×#239 | — | 3 | 2 | no | — |
| 105 | C2×#239 | — | 6 | 1 | no | — |
| 106 | C2×#239 | — | 9 | 8 | no | — |
| 107 | #1004 | — | 9 | 6 | no | — |
| 108 | C2×#235 | — | 9 | 6 | no | — |
| 109 | C22×C3×D3 | — | 3 | 6 | no | — |
| 110 | C22×C3×D3 | — | 6 | 3 | no | — |
| 111 | C2×D32 | — | 3 | 24 | no | — |
| 112 | C32×Q8 | — | 2 | 4 | no | — |
| 113 | C32×Q8 | C22×D3 | 1 | 8 | yes | — |
| 114 | C2×C32×C4 | — | 2 | 3 | no | — |
| 115 | C2×C32×C4 | C22×D3 | 1 | 6 | yes | — |
| 116 | #638 | C22×D3 | 1 | 8 | yes | — |
| 117 | C4⋊(C3⋊D3) | C22×D3 | 1 | 12 | yes | — |
| 118 | C4×C3⋊D3 | C22×D3 | 1 | 24 | yes | — |
| 119 | #634 | C22×D3 | 1 | 12 | yes | — |
| 120 | C3×#67 | — | 3 | 8 | no | — |
| 121 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 122 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 123 | C3×D12 | — | 3 | 12 | no | — |
| 124 | C3×D12 | — | 3 | 24 | no | — |
| 125 | C3×D12 | — | 6 | 12 | no | — |
| 126 | C3×C4×D3 | — | 3 | 24 | no | — |
| 127 | C3×C4×D3 | — | 3 | 12 | no | — |
| 128 | C3×C4×D3 | — | 3 | 12 | no | — |
| 129 | C3×C4×D3 | — | 6 | 6 | no | — |
| 130 | C3×C4×D3 | — | 6 | 6 | no | — |
| 131 | C3×Dic6 | — | 3 | 12 | no | — |
| 132 | #627 | — | 3 | 8 | no | — |
| 133 | #626 | — | 3 | 8 | no | — |
| 134 | #626 | — | 3 | 24 | no | — |
| 135 | #625 | — | 3 | 24 | no | — |
| 136 | #624 | — | 3 | 8 | no | — |
| 137 | D3×Dic3 | — | 3 | 8 | no | — |
| 138 | D3×Dic3 | — | 3 | 24 | no | — |
| 139 | #585 | — | 27 | 1 | no | Sylow |
| 140 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 141 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 142 | #272 | — | 2 | 6 | no | — |
| 143 | (C3⋊D3)⋊C3 | — | 2 | 8 | no | — |
| 144 | C3×#41 | — | 9 | 12 | no | — |
| 145 | C3×#41 | — | 9 | 8 | no | — |
| 146 | C3×#41 | — | 9 | 4 | no | — |
| 147 | C3×#41 | — | 9 | 4 | no | — |
| 148 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 149 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 150 | C2×C3×Q8 | — | 9 | 8 | no | — |
| 151 | C2×C3×Q8 | D32 | 1 | 1 | yes | characteristic |
| 152 | C2×C3×D4 | — | 9 | 3 | no | — |
| 153 | C22×C3×C4 | — | 9 | 3 | no | — |
| 154 | C2×#67 | — | 9 | 12 | no | — |
| 155 | #239 | — | 3 | 8 | no | — |
| 156 | #239 | — | 3 | 8 | no | — |
| 157 | #239 | — | 3 | 8 | no | — |
| 158 | #239 | — | 6 | 4 | no | — |
| 159 | #239 | — | 6 | 4 | no | — |
| 160 | #239 | — | 9 | 8 | no | — |
| 161 | #239 | — | 9 | 12 | no | — |
| 162 | #239 | — | 9 | 24 | no | — |
| 163 | D3×Q8 | — | 3 | 8 | no | — |
| 164 | D3×Q8 | — | 9 | 8 | no | — |
| 165 | D3×Q8 | — | 9 | 12 | no | — |
| 166 | #237 | — | 9 | 24 | no | — |
| 167 | #237 | — | 9 | 12 | no | — |
| 168 | #237 | — | 9 | 8 | no | — |
| 169 | D3×D4 | — | 9 | 24 | no | — |
| 170 | D3×D4 | — | 9 | 12 | no | — |
| 171 | D3×D4 | — | 9 | 24 | no | — |
| 172 | D3×D4 | — | 9 | 24 | no | — |
| 173 | #235 | — | 3 | 12 | no | — |
| 174 | #235 | — | 9 | 12 | no | — |
| 175 | #235 | — | 9 | 12 | no | — |
| 176 | #235 | — | 9 | 12 | no | — |
| 177 | #235 | — | 9 | 24 | no | — |
| 178 | #235 | — | 9 | 24 | no | — |
| 179 | #235 | — | 9 | 4 | no | — |
| 180 | C2×D12 | — | 3 | 6 | no | — |
| 181 | C2×D12 | — | 6 | 3 | no | — |
| 182 | C2×D12 | — | 9 | 6 | no | — |
| 183 | C2×D12 | — | 9 | 24 | no | — |
| 184 | C2×C4×D3 | — | 3 | 6 | no | — |
| 185 | C2×C4×D3 | — | 6 | 3 | no | — |
| 186 | C2×C4×D3 | — | 9 | 12 | no | — |
| 187 | C2×C4×D3 | — | 9 | 24 | no | — |
| 188 | C2×Dic6 | — | 9 | 6 | no | — |
| 189 | C22×C32 | — | 2 | 1 | no | — |
| 190 | C22×C32 | C23×D3 | 1 | 2 | yes | — |
| 191 | C2×C3⋊D3 | C23×D3 | 1 | 8 | yes | — |
| 192 | C2×C3×D3 | — | 3 | 8 | no | — |
| 193 | C2×C3×D3 | — | 3 | 12 | no | — |
| 194 | C2×C3×D3 | — | 6 | 6 | no | — |
| 195 | C2×C3×D3 | — | 12 | 6 | no | — |
| 196 | C2×C3×D3 | — | 12 | 6 | no | — |
| 197 | D32 | — | 12 | 24 | no | — |
| 198 | C32×C4 | — | 2 | 6 | no | — |
| 199 | C32×C4 | C23×D3 | 1 | 12 | yes | — |
| 200 | C3⋊Dic3 | C23×D3 | 1 | 8 | yes | — |
| 201 | C3×Dic3 | — | 3 | 8 | no | — |
| 202 | C3×Dic3 | — | 3 | 2 | no | — |
| 203 | C3×Dic3 | — | 3 | 2 | no | — |
| 204 | C3×Dic3 | — | 6 | 1 | no | — |
| 205 | C3×Dic3 | — | 6 | 1 | no | — |
| 206 | 2−1+4 | — | 9 | 2 | no | — |
| 207 | 2−1+4 | — | 27 | 4 | no | — |
| 208 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 209 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 210 | C2×#41 | — | 9 | 1 | no | — |
| 211 | C2×#41 | — | 27 | 6 | no | — |
| 212 | C2×#41 | — | 27 | 8 | no | — |
| 213 | H(3,𝔽3) | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | C23×C3 | — | 9 | 3 | no | — |
| 215 | C22×D3 | — | 3 | 6 | no | — |
| 216 | C22×D3 | — | 6 | 3 | no | — |
| 217 | C22×D3 | — | 9 | 12 | no | — |
| 218 | C22×D3 | — | 9 | 24 | no | — |
| 219 | C3×Q8 | — | 3 | 8 | no | — |
| 220 | C3×Q8 | — | 6 | 4 | no | — |
| 221 | C3×Q8 | — | 9 | 12 | no | — |
| 222 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 223 | C3×D4 | — | 9 | 12 | no | — |
| 224 | C3×D4 | — | 9 | 8 | no | — |
| 225 | C3×D4 | — | 9 | 12 | no | — |
| 226 | C2×C3×C4 | — | 3 | 6 | no | — |
| 227 | C2×C3×C4 | — | 6 | 3 | no | — |
| 228 | C2×C3×C4 | — | 9 | 24 | no | — |
| 229 | C2×C3×C4 | — | 9 | 1 | no | — |
| 230 | C2×C3×C4 | — | 9 | 6 | no | — |
| 231 | C2×C3×C4 | — | 9 | 6 | no | — |
| 232 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 233 | #67 | — | 3 | 8 | no | — |
| 234 | #67 | — | 9 | 8 | no | — |
| 235 | #67 | — | 9 | 24 | no | — |
| 236 | #67 | — | 9 | 8 | no | — |
| 237 | #67 | — | 9 | 24 | no | — |
| 238 | C2×Dic3 | — | 3 | 2 | no | — |
| 239 | C2×Dic3 | — | 6 | 1 | no | — |
| 240 | C2×Dic3 | — | 9 | 12 | no | — |
| 241 | C2×Dic3 | — | 9 | 8 | no | — |
| 242 | D12 | — | 3 | 24 | no | — |
| 243 | D12 | — | 3 | 12 | no | — |
| 244 | D12 | — | 6 | 12 | no | — |
| 245 | D12 | — | 9 | 12 | no | — |
| 246 | D12 | — | 9 | 4 | no | — |
| 247 | D12 | — | 9 | 24 | no | — |
| 248 | C4×D3 | — | 3 | 12 | no | — |
| 249 | C4×D3 | — | 3 | 12 | no | — |
| 250 | C4×D3 | — | 3 | 24 | no | — |
| 251 | C4×D3 | — | 6 | 6 | no | — |
| 252 | C4×D3 | — | 6 | 6 | no | — |
| 253 | C4×D3 | — | 9 | 24 | no | — |
| 254 | C4×D3 | — | 9 | 8 | no | — |
| 255 | C4×D3 | — | 9 | 8 | no | — |
| 256 | C4×D3 | — | 9 | 24 | no | — |
| 257 | Dic6 | — | 3 | 12 | no | — |
| 258 | Dic6 | — | 9 | 12 | no | — |
| 259 | Dic6 | — | 9 | 4 | no | — |
| 260 | Dic6 | — | 9 | 8 | no | — |
| 261 | C2×C32 | — | 2 | 2 | no | — |
| 262 | C2×C32 | — | 2 | 2 | no | — |
| 263 | C2×C32 | — | 2 | 1 | no | — |
| 264 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 265 | C3⋊D3 | — | 2 | 8 | no | — |
| 266 | C3×D3 | — | 6 | 8 | no | — |
| 267 | C3×D3 | — | 6 | 12 | no | — |
| 268 | C3×D3 | — | 12 | 6 | no | — |
| 269 | #41 | — | 9 | 4 | no | — |
| 270 | #41 | — | 9 | 4 | no | — |
| 271 | #41 | — | 9 | 8 | no | — |
| 272 | #41 | — | 9 | 12 | no | — |
| 273 | #41 | — | 27 | 12 | no | — |
| 274 | #41 | — | 27 | 4 | no | — |
| 275 | #41 | — | 27 | 12 | no | — |
| 276 | #41 | — | 27 | 24 | no | — |
| 277 | C2×Q8 | — | 9 | 8 | no | — |
| 278 | C2×Q8 | — | 27 | 6 | no | — |
| 279 | C2×Q8 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 280 | C2×D4 | — | 9 | 3 | no | — |
| 281 | C2×D4 | — | 27 | 6 | no | — |
| 282 | C2×D4 | — | 27 | 24 | no | — |
| 283 | C2×D4 | — | 27 | 12 | no | — |
| 284 | C22×C4 | — | 9 | 3 | no | — |
| 285 | C22×C4 | — | 27 | 12 | no | — |
| 286 | C22×C3 | — | 3 | 2 | no | — |
| 287 | C22×C3 | — | 6 | 1 | no | — |
| 288 | C22×C3 | — | 9 | 8 | no | — |
| 289 | C22×C3 | — | 9 | 6 | no | — |
| 290 | C22×C3 | — | 36 | 3 | no | — |
| 291 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 292 | C2×D3 | — | 3 | 12 | no | — |
| 293 | C2×D3 | — | 3 | 8 | no | — |
| 294 | C2×D3 | — | 6 | 6 | no | — |
| 295 | C2×D3 | — | 9 | 8 | no | — |
| 296 | C2×D3 | — | 12 | 6 | no | — |
| 297 | C2×D3 | — | 12 | 6 | no | — |
| 298 | C2×D3 | — | 36 | 12 | no | — |
| 299 | C2×D3 | — | 36 | 24 | no | — |
| 300 | C3×C4 | — | 3 | 12 | no | — |
| 301 | C3×C4 | — | 6 | 6 | no | — |
| 302 | C3×C4 | — | 9 | 8 | no | — |
| 303 | C3×C4 | — | 9 | 1 | no | — |
| 304 | C3×C4 | — | 9 | 1 | no | — |
| 305 | C3×C4 | C22×D32 | 1 | 6 | yes | — |
| 306 | Dic3 | — | 3 | 2 | no | — |
| 307 | Dic3 | — | 3 | 2 | no | — |
| 308 | Dic3 | — | 3 | 8 | no | — |
| 309 | Dic3 | — | 6 | 1 | no | — |
| 310 | Dic3 | — | 6 | 1 | no | — |
| 311 | Dic3 | — | 9 | 8 | no | — |
| 312 | C32 | — | 2 | 1 | no | — |
| 313 | C32 | #5968 | 1 | 2 | yes | complemented |
| 314 | C23 | — | 9 | 3 | no | — |
| 315 | C23 | — | 27 | 12 | no | — |
| 316 | Q8 | — | 9 | 12 | no | — |
| 317 | Q8 | — | 27 | 4 | no | — |
| 318 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 4 | yes | — |
| 319 | D4 | — | 9 | 8 | no | — |
| 320 | D4 | — | 9 | 12 | no | — |
| 321 | D4 | — | 9 | 12 | no | — |
| 322 | D4 | — | 27 | 4 | no | — |
| 323 | D4 | — | 27 | 24 | no | — |
| 324 | C2×C4 | — | 9 | 1 | no | — |
| 325 | C2×C4 | — | 9 | 6 | no | — |
| 326 | C2×C4 | — | 9 | 6 | no | — |
| 327 | C2×C4 | — | 9 | 24 | no | — |
| 328 | C2×C4 | — | 27 | 8 | no | — |
| 329 | C2×C4 | — | 27 | 12 | no | — |
| 330 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 331 | C2×C3 | — | 2 | 1 | no | — |
| 332 | C2×C3 | — | 3 | 2 | no | — |
| 333 | C2×C3 | — | 6 | 2 | no | — |
| 334 | C2×C3 | — | 6 | 2 | no | — |
| 335 | C2×C3 | — | 6 | 1 | no | — |
| 336 | C2×C3 | — | 18 | 8 | no | — |
| 337 | C2×C3 | — | 18 | 6 | no | — |
| 338 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 339 | D3 | — | 6 | 12 | no | — |
| 340 | D3 | — | 6 | 8 | no | — |
| 341 | D3 | — | 12 | 6 | no | — |
| 342 | D3 | — | 18 | 8 | no | — |
| 343 | C22 | — | 9 | 8 | no | — |
| 344 | C22 | — | 9 | 6 | no | — |
| 345 | C22 | — | 36 | 3 | no | — |
| 346 | C22 | — | 108 | 12 | no | — |
| 347 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 348 | C4 | — | 9 | 1 | no | — |
| 349 | C4 | — | 9 | 1 | no | — |
| 350 | C4 | — | 9 | 8 | no | — |
| 351 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 6 | yes | — |
| 352 | C3 | — | 3 | 2 | no | — |
| 353 | C3 | — | 6 | 1 | no | — |
| 354 | C3 | #10596689 | 1 | 1 | yes | characteristic |
| 355 | C2 | — | 2 | 1 | no | — |
| 356 | C2 | — | 18 | 6 | no | — |
| 357 | C2 | — | 18 | 8 | no | — |
| 358 | C2 | C23×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88748 | C2 | semidirect |
| 2. #11722627 | C2 | semidirect |
| 3. #11722521 | C2 | semidirect |
| 4. #11722519 | C2 | semidirect |
| 5. #11722517 | C2 | semidirect |
| 6. #11722493 | C2 | semidirect |
| 7. #11722491 | C2 | semidirect |
| 9. C2×Q8×H(3,𝔽3) | C22 | semidirect |
| 10. #88748 | C22 | semidirect |
| 11. #88748 | C22 | semidirect |
| 12. C2×C4⋊#272 | C22 | semidirect |
| 13. C2×C4×#272 | C22 | semidirect |
| 14. #88722 | C22 | semidirect |
| 15. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 16. #3828⋊C3 | C22 | semidirect |
| 17. #88677 | C22 | semidirect |
| 18. #88672 | C22 | semidirect |
| 19. #88655 | C22 | semidirect |
| 20. #88654 | C22 | semidirect |
| 21. C4×((C3⋊D3)⋊C3)⋊C2 | C22 | semidirect |
| 22. #88652 | C22 | semidirect |
| 23. #88651 | C22 | semidirect |
| 24. #88650 | C22 | semidirect |
| 25. #88649 | C22 | semidirect |
| 26. #64364 | D3 | semidirect |
| 56. C2×C32×Q8 | C2×D3 | semidirect |
| 57. #3832 | C2×D3 | semidirect |
| 58. Q8×C3⋊D3 | C2×D3 | semidirect |
| 59. #3828 | C2×D3 | semidirect |
| 213. H(3,𝔽3) | #585 | semidirect |
| 279. C2×Q8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 313. C32 | #5968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88748 | 2 |
| #11722627 | 2 |
| #11722521 | 2 |
| #11722519 | 2 |
| #11722517 | 2 |
| #11722493 | 2 |
| #11722491 | 2 |
| #10596688 | 3 |