Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1007 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1007 conjugacy classes of subgroups — too many to draw. Only its 135 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 | #11722505 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | D8×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64121⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11721197 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11721188 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11720850 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C8×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11720833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D3×#912 | — | 3 | 2 | no | maximal |
| 10 | D4×#272 | C22 | 1 | 2 | yes | — |
| 11 | #3830⋊C3 | C22 | 1 | 4 | yes | complemented |
| 12 | #88677 | — | 2 | 2 | no | — |
| 13 | C2×#6199 | — | 2 | 2 | no | — |
| 14 | #88671 | — | 2 | 4 | no | — |
| 15 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 16 | #88652 | C22 | 1 | 4 | yes | complemented |
| 17 | #88651 | C22 | 1 | 2 | yes | — |
| 18 | D8×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #88545 | C22 | 1 | 2 | yes | complemented |
| 20 | #88529 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C8×#272 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3754⋊C3 | C22 | 1 | 4 | yes | complemented |
| 23 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 24 | #3746⋊C3 | C22 | 1 | 2 | yes | complemented |
| 25 | #88437 | C22 | 1 | 4 | yes | complemented |
| 26 | #88434 | C22 | 1 | 1 | yes | characteristic |
| 27 | #88433 | C22 | 1 | 2 | yes | complemented |
| 28 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 2 | yes | complemented |
| 29 | D3×#237 | — | 3 | 4 | no | — |
| 30 | #64121 | D3 | 1 | 2 | yes | complemented |
| 31 | C3×#912 | — | 3 | 2 | no | — |
| 32 | C3×D3×D8 | — | 3 | 2 | no | — |
| 33 | C3×D3×D8 | — | 6 | 1 | no | — |
| 34 | #63936 | — | 3 | 4 | no | — |
| 35 | #63933 | — | 3 | 4 | no | — |
| 36 | D3×#214 | — | 3 | 4 | no | — |
| 37 | #63810 | — | 3 | 2 | no | — |
| 38 | #63807 | — | 3 | 2 | no | — |
| 39 | D3×Dic12 | — | 3 | 2 | no | — |
| 40 | D32×C8 | — | 3 | 2 | no | — |
| 41 | C22×#272 | — | 2 | 2 | no | — |
| 42 | C2×((C3⋊D3)⋊C3)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 43 | D4×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 44 | #6235 | — | 2 | 2 | no | — |
| 45 | C4⋊#272 | C23 | 1 | 2 | yes | — |
| 46 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 47 | #638⋊C3 | — | 2 | 4 | no | — |
| 48 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 4 | no | — |
| 49 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 50 | #634⋊C3 | C23 | 1 | 4 | yes | — |
| 51 | #6200 | — | 2 | 4 | no | — |
| 52 | #6199 | — | 2 | 2 | no | — |
| 53 | #6199 | — | 2 | 4 | no | — |
| 54 | #6199 | D4 | 1 | 1 | yes | characteristic |
| 55 | ((C3⋊D3)⋊C3)⋊C4 | D4 | 1 | 2 | yes | — |
| 56 | #6196 | — | 2 | 2 | no | — |
| 57 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 58 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 59 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 60 | D3×#135 | — | 9 | 2 | no | — |
| 61 | C2×#912 | — | 9 | 1 | no | — |
| 62 | #3830 | C2×D3 | 1 | 4 | yes | complemented |
| 63 | C3×#237 | — | 3 | 4 | no | — |
| 64 | C3×D3×D4 | — | 3 | 4 | no | — |
| 65 | C3×D3×D4 | — | 6 | 2 | no | — |
| 66 | D3×#67 | — | 6 | 4 | no | — |
| 67 | #3805 | — | 6 | 4 | no | — |
| 68 | #3804 | — | 6 | 4 | no | — |
| 69 | C2×D3×Dic3 | — | 6 | 4 | no | — |
| 70 | C4×D32 | — | 3 | 2 | no | — |
| 71 | #3796 | — | 3 | 4 | no | — |
| 72 | #3795 | — | 3 | 4 | no | — |
| 73 | D3×Dic6 | — | 3 | 4 | no | — |
| 74 | C32×D8 | — | 2 | 1 | no | — |
| 75 | C32×D8 | C2×D3 | 1 | 2 | yes | complemented |
| 76 | #3754 | C2×D3 | 1 | 4 | yes | complemented |
| 77 | #3746 | C2×D3 | 1 | 2 | yes | complemented |
| 78 | C8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 79 | C3×#214 | — | 3 | 4 | no | — |
| 80 | C3×#213 | — | 3 | 4 | no | — |
| 81 | C3×#213 | — | 6 | 2 | no | — |
| 82 | C3×Dic12 | — | 3 | 2 | no | — |
| 83 | C3×D24 | — | 3 | 2 | no | — |
| 84 | C3×D24 | — | 6 | 1 | no | — |
| 85 | C3×D3×C8 | — | 3 | 2 | no | — |
| 86 | C3×D3×C8 | — | 3 | 2 | no | — |
| 87 | C3×D3×C8 | — | 6 | 1 | no | — |
| 88 | #3719 | — | 3 | 4 | no | — |
| 89 | #3716 | — | 3 | 4 | no | — |
| 90 | #3715 | — | 3 | 4 | no | — |
| 91 | #3710 | — | 3 | 2 | no | — |
| 92 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 93 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 94 | C22×H(3,𝔽3) | — | 2 | 2 | no | — |
| 95 | C2×#272 | — | 2 | 2 | no | — |
| 96 | C2×#272 | — | 4 | 4 | no | — |
| 97 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 99 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 100 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 101 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | (C3⋊Dic3)⋊C3 | — | 2 | 4 | no | — |
| 103 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 104 | D3×#41 | — | 9 | 4 | no | — |
| 105 | C2×#237 | — | 9 | 2 | no | — |
| 106 | C3×#135 | — | 9 | 2 | no | — |
| 107 | C2×C3×D8 | — | 9 | 1 | no | — |
| 108 | #950 | — | 9 | 4 | no | — |
| 109 | C2×#214 | — | 9 | 2 | no | — |
| 110 | #919 | — | 9 | 2 | no | — |
| 111 | D3×Q16 | — | 9 | 2 | no | — |
| 112 | #916 | — | 9 | 4 | no | — |
| 113 | D3×SD16 | — | 9 | 4 | no | — |
| 114 | #912 | — | 3 | 2 | no | — |
| 115 | #912 | — | 9 | 2 | no | — |
| 116 | #912 | — | 9 | 2 | no | — |
| 117 | #912 | — | 9 | 4 | no | — |
| 118 | D3×D8 | — | 3 | 2 | no | — |
| 119 | D3×D8 | — | 6 | 1 | no | — |
| 120 | C2×Dic12 | — | 9 | 1 | no | — |
| 121 | #904 | — | 9 | 2 | no | — |
| 122 | C2×D3×C8 | — | 9 | 1 | no | — |
| 123 | C2×D3×C8 | — | 9 | 2 | no | — |
| 124 | C22×C3×D3 | — | 6 | 4 | no | — |
| 125 | C22×C3×D3 | — | 12 | 2 | no | — |
| 126 | C2×D32 | — | 3 | 2 | no | — |
| 127 | C32×D4 | — | 2 | 2 | no | — |
| 128 | C32×D4 | C22×D3 | 1 | 4 | yes | — |
| 129 | #638 | — | 2 | 4 | no | — |
| 130 | C2×C3⋊Dic3 | — | 2 | 4 | no | — |
| 131 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 132 | #634 | C22×D3 | 1 | 4 | yes | — |
| 133 | C3×#67 | — | 6 | 4 | no | — |
| 134 | C3×#67 | — | 6 | 4 | no | — |
| 135 | C3×#67 | — | 12 | 2 | no | — |
| 136 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 137 | C3×D12 | — | 3 | 4 | no | — |
| 138 | C3×D12 | — | 6 | 2 | no | — |
| 139 | C3×C4×D3 | — | 3 | 2 | no | — |
| 140 | C3×C4×D3 | — | 3 | 2 | no | — |
| 141 | C3×C4×D3 | — | 6 | 1 | no | — |
| 142 | C3×Dic6 | — | 3 | 4 | no | — |
| 143 | #627 | — | 6 | 4 | no | — |
| 144 | #626 | — | 6 | 4 | no | — |
| 145 | #625 | — | 6 | 4 | no | — |
| 146 | #624 | — | 3 | 2 | no | — |
| 147 | D3×Dic3 | — | 3 | 2 | no | — |
| 148 | D3×Dic3 | — | 3 | 2 | no | — |
| 149 | D3×Dic3 | — | 6 | 4 | no | — |
| 150 | D3×Dic3 | — | 6 | 4 | no | — |
| 151 | D3×Dic3 | — | 6 | 4 | no | — |
| 152 | C32×C8 | — | 2 | 1 | no | — |
| 153 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 154 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 155 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 156 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 157 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 158 | C2×#135 | — | 27 | 1 | no | Sylow |
| 159 | C2×H(3,𝔽3) | — | 4 | 2 | no | — |
| 160 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 161 | #272 | — | 4 | 2 | no | — |
| 162 | #272 | #135 | 1 | 2 | yes | complemented |
| 163 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 164 | C3×#41 | — | 9 | 4 | no | — |
| 165 | C2×C3×D4 | — | 9 | 2 | no | — |
| 166 | C2×#67 | — | 18 | 2 | no | — |
| 167 | C22×Dic3 | — | 18 | 2 | no | — |
| 168 | #239 | — | 9 | 4 | no | — |
| 169 | D3×Q8 | — | 9 | 4 | no | — |
| 170 | #237 | — | 3 | 4 | no | — |
| 171 | #237 | — | 9 | 4 | no | — |
| 172 | #237 | — | 9 | 4 | no | — |
| 173 | #237 | — | 18 | 4 | no | — |
| 174 | #237 | — | 18 | 4 | no | — |
| 175 | D3×D4 | — | 3 | 4 | no | — |
| 176 | D3×D4 | — | 6 | 2 | no | — |
| 177 | D3×D4 | — | 18 | 4 | no | — |
| 178 | #235 | — | 9 | 4 | no | — |
| 179 | #235 | — | 18 | 4 | no | — |
| 180 | C2×C4×D3 | — | 9 | 1 | no | — |
| 181 | C2×C4×D3 | — | 9 | 2 | no | — |
| 182 | C2×C4×D3 | — | 18 | 4 | no | — |
| 183 | C2×Dic6 | — | 9 | 2 | no | — |
| 184 | C3×Q16 | — | 9 | 2 | no | — |
| 185 | C3×SD16 | — | 9 | 4 | no | — |
| 186 | C3×D8 | — | 3 | 2 | no | — |
| 187 | C3×D8 | — | 6 | 1 | no | — |
| 188 | C3×D8 | — | 9 | 2 | no | — |
| 189 | C3×D8 | — | 9 | 1 | no | — |
| 190 | C3×D8 | D32 | 1 | 1 | yes | characteristic |
| 191 | C2×C3×C8 | — | 9 | 2 | no | — |
| 192 | C2×C3×C8 | — | 9 | 1 | no | — |
| 193 | #216 | — | 9 | 4 | no | — |
| 194 | #215 | — | 9 | 4 | no | — |
| 195 | #214 | — | 3 | 4 | no | — |
| 196 | #214 | — | 9 | 4 | no | — |
| 197 | #214 | — | 9 | 4 | no | — |
| 198 | #213 | — | 3 | 4 | no | — |
| 199 | #213 | — | 6 | 2 | no | — |
| 200 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 201 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 202 | Dic12 | — | 3 | 2 | no | — |
| 203 | Dic12 | — | 9 | 2 | no | — |
| 204 | Dic12 | — | 9 | 2 | no | — |
| 205 | D24 | — | 3 | 2 | no | — |
| 206 | D24 | — | 6 | 1 | no | — |
| 207 | #204 | — | 9 | 4 | no | — |
| 208 | D3×C8 | — | 3 | 2 | no | — |
| 209 | D3×C8 | — | 3 | 2 | no | — |
| 210 | D3×C8 | — | 6 | 1 | no | — |
| 211 | D3×C8 | — | 9 | 2 | no | — |
| 212 | D3×C8 | — | 9 | 2 | no | — |
| 213 | D3×C8 | — | 9 | 2 | no | — |
| 214 | D3×C8 | — | 9 | 2 | no | — |
| 215 | C22×C32 | — | 2 | 4 | no | — |
| 216 | C22×C32 | — | 4 | 2 | no | — |
| 217 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 218 | C2×C3×D3 | — | 3 | 2 | no | — |
| 219 | C2×C3×D3 | — | 3 | 2 | no | — |
| 220 | C2×C3×D3 | — | 6 | 1 | no | — |
| 221 | C2×C3×D3 | — | 6 | 4 | no | — |
| 222 | C2×C3×D3 | — | 12 | 2 | no | — |
| 223 | C2×C3×D3 | — | 12 | 8 | no | — |
| 224 | C2×C3×D3 | — | 24 | 4 | no | — |
| 225 | D32 | — | 6 | 4 | no | — |
| 226 | C32×C4 | — | 2 | 1 | no | — |
| 227 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 228 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 229 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 230 | C3×Dic3 | — | 3 | 2 | no | — |
| 231 | C3×Dic3 | — | 3 | 2 | no | — |
| 232 | C3×Dic3 | — | 6 | 1 | no | — |
| 233 | C3×Dic3 | — | 6 | 4 | no | — |
| 234 | C2×#41 | — | 27 | 2 | no | — |
| 235 | #135 | — | 9 | 2 | no | — |
| 236 | #135 | — | 27 | 2 | no | — |
| 237 | #135 | — | 27 | 4 | no | — |
| 238 | C2×Q16 | — | 27 | 1 | no | — |
| 239 | C2×SD16 | — | 27 | 2 | no | — |
| 240 | C2×D8 | — | 9 | 1 | no | — |
| 241 | C22×C8 | — | 27 | 1 | no | — |
| 242 | H(3,𝔽3) | C2×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 243 | C23×C3 | — | 18 | 2 | no | — |
| 244 | C22×D3 | — | 6 | 4 | no | — |
| 245 | C22×D3 | — | 9 | 1 | no | — |
| 246 | C22×D3 | — | 9 | 2 | no | — |
| 247 | C22×D3 | — | 12 | 2 | no | — |
| 248 | C3×Q8 | — | 9 | 4 | no | — |
| 249 | C3×D4 | — | 3 | 4 | no | — |
| 250 | C3×D4 | — | 6 | 2 | no | — |
| 251 | C3×D4 | — | 9 | 2 | no | — |
| 252 | C3×D4 | — | 18 | 2 | no | — |
| 253 | C3×D4 | — | 18 | 4 | no | — |
| 254 | C3×D4 | C2×D32 | 1 | 2 | yes | — |
| 255 | C2×C3×C4 | — | 9 | 2 | no | — |
| 256 | C2×C3×C4 | — | 9 | 1 | no | — |
| 257 | C2×C3×C4 | — | 18 | 4 | no | — |
| 258 | #67 | — | 6 | 4 | no | — |
| 259 | #67 | — | 6 | 4 | no | — |
| 260 | #67 | — | 12 | 2 | no | — |
| 261 | #67 | — | 18 | 4 | no | — |
| 262 | #67 | — | 18 | 4 | no | — |
| 263 | #67 | — | 18 | 4 | no | — |
| 264 | C2×Dic3 | — | 6 | 4 | no | — |
| 265 | C2×Dic3 | — | 9 | 1 | no | — |
| 266 | C2×Dic3 | — | 9 | 2 | no | — |
| 267 | C2×Dic3 | — | 18 | 4 | no | — |
| 268 | C2×Dic3 | — | 18 | 4 | no | — |
| 269 | C2×Dic3 | — | 18 | 2 | no | — |
| 270 | D12 | — | 3 | 4 | no | — |
| 271 | D12 | — | 6 | 2 | no | — |
| 272 | D12 | — | 18 | 4 | no | — |
| 273 | C4×D3 | — | 3 | 2 | no | — |
| 274 | C4×D3 | — | 3 | 2 | no | — |
| 275 | C4×D3 | — | 6 | 1 | no | — |
| 276 | C4×D3 | — | 9 | 2 | no | — |
| 277 | C4×D3 | — | 9 | 2 | no | — |
| 278 | C4×D3 | — | 9 | 2 | no | — |
| 279 | C4×D3 | — | 9 | 2 | no | — |
| 280 | C4×D3 | — | 18 | 4 | no | — |
| 281 | C4×D3 | — | 18 | 4 | no | — |
| 282 | C4×D3 | — | 18 | 4 | no | — |
| 283 | Dic6 | — | 3 | 4 | no | — |
| 284 | Dic6 | — | 9 | 4 | no | — |
| 285 | Dic6 | — | 18 | 4 | no | — |
| 286 | Dic6 | — | 18 | 2 | no | — |
| 287 | C3×C8 | — | 3 | 2 | no | — |
| 288 | C3×C8 | — | 6 | 1 | no | — |
| 289 | C3×C8 | — | 9 | 2 | no | — |
| 290 | C3×C8 | — | 9 | 1 | no | — |
| 291 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 292 | C3⋊C8 | — | 3 | 2 | no | — |
| 293 | C3⋊C8 | — | 3 | 2 | no | — |
| 294 | C3⋊C8 | — | 6 | 1 | no | — |
| 295 | C3⋊C8 | — | 9 | 2 | no | — |
| 296 | C2×C32 | — | 2 | 1 | no | — |
| 297 | C2×C32 | — | 4 | 4 | no | — |
| 298 | C2×C32 | — | 8 | 2 | no | — |
| 299 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 300 | C3⋊D3 | — | 2 | 2 | no | — |
| 301 | C3×D3 | — | 3 | 4 | no | — |
| 302 | C3×D3 | — | 6 | 2 | no | — |
| 303 | C3×D3 | — | 6 | 2 | no | — |
| 304 | C3×D3 | — | 12 | 4 | no | — |
| 305 | C3×D3 | — | 24 | 2 | no | — |
| 306 | #41 | — | 9 | 4 | no | — |
| 307 | #41 | — | 27 | 4 | no | — |
| 308 | #41 | — | 54 | 4 | no | — |
| 309 | C2×Q8 | — | 27 | 2 | no | — |
| 310 | C2×D4 | — | 9 | 2 | no | — |
| 311 | C2×D4 | — | 54 | 2 | no | — |
| 312 | C22×C4 | — | 27 | 1 | no | — |
| 313 | C22×C4 | — | 54 | 2 | no | — |
| 314 | Q16 | — | 9 | 2 | no | — |
| 315 | Q16 | — | 27 | 2 | no | — |
| 316 | SD16 | — | 9 | 4 | no | — |
| 317 | SD16 | — | 27 | 4 | no | — |
| 318 | D8 | — | 9 | 2 | no | — |
| 319 | D8 | — | 9 | 1 | no | — |
| 320 | D8 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 321 | C2×C8 | — | 9 | 1 | no | — |
| 322 | C2×C8 | — | 9 | 2 | no | — |
| 323 | C2×C8 | — | 27 | 1 | no | — |
| 324 | C2×C8 | — | 27 | 2 | no | — |
| 325 | C22×C3 | — | 2 | 2 | no | — |
| 326 | C22×C3 | — | 6 | 4 | no | — |
| 327 | C22×C3 | — | 9 | 2 | no | — |
| 328 | C22×C3 | — | 9 | 1 | no | — |
| 329 | C22×C3 | — | 12 | 2 | no | — |
| 330 | C22×C3 | — | 18 | 2 | no | — |
| 331 | C22×C3 | — | 36 | 4 | no | — |
| 332 | C2×D3 | — | 3 | 2 | no | — |
| 333 | C2×D3 | — | 3 | 2 | no | — |
| 334 | C2×D3 | — | 6 | 1 | no | — |
| 335 | C2×D3 | — | 6 | 4 | no | — |
| 336 | C2×D3 | — | 9 | 2 | no | — |
| 337 | C2×D3 | — | 12 | 2 | no | — |
| 338 | C2×D3 | — | 12 | 8 | no | — |
| 339 | C2×D3 | — | 18 | 4 | no | — |
| 340 | C2×D3 | — | 18 | 2 | no | — |
| 341 | C2×D3 | — | 24 | 4 | no | — |
| 342 | C3×C4 | — | 3 | 2 | no | — |
| 343 | C3×C4 | — | 6 | 1 | no | — |
| 344 | C3×C4 | — | 9 | 2 | no | — |
| 345 | C3×C4 | — | 9 | 1 | no | — |
| 346 | C3×C4 | — | 18 | 4 | no | — |
| 347 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 348 | Dic3 | — | 3 | 2 | no | — |
| 349 | Dic3 | — | 3 | 2 | no | — |
| 350 | Dic3 | — | 6 | 1 | no | — |
| 351 | Dic3 | — | 6 | 4 | no | — |
| 352 | Dic3 | — | 9 | 2 | no | — |
| 353 | Dic3 | — | 18 | 4 | no | — |
| 354 | C32 | — | 2 | 1 | no | — |
| 355 | C32 | D3×#135 | 1 | 2 | yes | complemented |
| 356 | C23 | — | 18 | 2 | no | — |
| 357 | C23 | — | 27 | 1 | no | — |
| 358 | Q8 | — | 9 | 4 | no | — |
| 359 | Q8 | — | 54 | 2 | no | — |
| 360 | D4 | — | 9 | 2 | no | — |
| 361 | D4 | — | 18 | 2 | no | — |
| 362 | D4 | — | 18 | 4 | no | — |
| 363 | D4 | — | 54 | 4 | no | — |
| 364 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 365 | C2×C4 | — | 9 | 1 | no | — |
| 366 | C2×C4 | — | 9 | 2 | no | — |
| 367 | C2×C4 | — | 18 | 4 | no | — |
| 368 | C2×C4 | — | 27 | 1 | no | — |
| 369 | C2×C4 | — | 27 | 2 | no | — |
| 370 | C2×C4 | — | 54 | 4 | no | — |
| 371 | C2×C4 | — | 54 | 2 | no | — |
| 372 | C8 | — | 9 | 1 | no | — |
| 373 | C8 | — | 9 | 2 | no | — |
| 374 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 375 | C2×C3 | — | 3 | 2 | no | — |
| 376 | C2×C3 | — | 4 | 2 | no | — |
| 377 | C2×C3 | — | 6 | 1 | no | — |
| 378 | C2×C3 | — | 9 | 2 | no | — |
| 379 | C2×C3 | — | 12 | 4 | no | — |
| 380 | C2×C3 | — | 18 | 2 | no | — |
| 381 | C2×C3 | — | 24 | 2 | no | — |
| 382 | C2×C3 | — | 36 | 2 | no | — |
| 383 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 384 | D3 | — | 3 | 4 | no | — |
| 385 | D3 | — | 6 | 2 | no | — |
| 386 | D3 | — | 6 | 2 | no | — |
| 387 | D3 | — | 12 | 4 | no | — |
| 388 | D3 | — | 18 | 2 | no | — |
| 389 | D3 | — | 24 | 2 | no | — |
| 390 | C22 | — | 2 | 2 | no | — |
| 391 | C22 | — | 9 | 1 | no | — |
| 392 | C22 | — | 9 | 2 | no | — |
| 393 | C22 | — | 18 | 2 | no | — |
| 394 | C22 | — | 36 | 4 | no | — |
| 395 | C22 | — | 54 | 2 | no | — |
| 396 | C4 | — | 9 | 2 | no | — |
| 397 | C4 | — | 9 | 1 | no | — |
| 398 | C4 | — | 18 | 4 | no | — |
| 399 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 400 | C3 | — | 3 | 2 | no | — |
| 401 | C3 | — | 6 | 1 | no | — |
| 402 | C3 | #10594730 | 1 | 1 | yes | characteristic |
| 403 | C2 | — | 4 | 2 | no | — |
| 404 | C2 | — | 9 | 2 | no | — |
| 405 | C2 | — | 18 | 2 | no | — |
| 406 | C2 | — | 36 | 2 | no | — |
| 407 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722505 | C2 | semidirect |
| 2. D8×#272 | C2 | semidirect |
| 3. #64121⋊C3 | C2 | semidirect |
| 4. #11721197 | C2 | semidirect |
| 5. #11721188 | C2 | semidirect |
| 6. #11720850 | C2 | semidirect |
| 7. C8×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 8. #11720833 | C2 | semidirect |
| 11. #3830⋊C3 | C22 | semidirect |
| 16. #88652 | C22 | semidirect |
| 18. D8×H(3,𝔽3) | C22 | semidirect |
| 19. #88545 | C22 | semidirect |
| 20. #88529 | C22 | semidirect |
| 22. #3754⋊C3 | C22 | semidirect |
| 23. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 24. #3746⋊C3 | C22 | semidirect |
| 25. #88437 | C22 | semidirect |
| 27. #88433 | C22 | semidirect |
| 28. ((C3⋊D3)⋊C3)⋊C8 | C22 | semidirect |
| 30. #64121 | D3 | semidirect |
| 62. #3830 | C2×D3 | semidirect |
| 75. C32×D8 | C2×D3 | semidirect |
| 76. #3754 | C2×D3 | semidirect |
| 77. #3746 | C2×D3 | semidirect |
| 78. C8×C3⋊D3 | C2×D3 | semidirect |
| 162. #272 | #135 | semidirect |
| 242. H(3,𝔽3) | C2×#135 | semidirect |
| 320. D8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 355. C32 | D3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722505 | 2 |
| D8×#272 | 2 |
| #64121⋊C3 | 2 |
| #11721197 | 2 |
| #11721188 | 2 |
| #11720850 | 2 |
| C8×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #11720833 | 2 |
| D3×#912 | 3 |