Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601476 | C2 | semidirect |
| 2. #22598061 | C2 | semidirect |
| 3. #22598003 | C2 | semidirect |
| 4. C2×#17985808 | C2 | semidirect |
| 5. #22590067 | C2 | semidirect |
| 6. #22589967 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 50. C2×Dic284 | D4 | semidirect |
| 54. C2×D568 | D4 | semidirect |
| 83. C2×C16×C71 | D4 | semidirect |
| 85. #108×C71 | D4 | semidirect |
| 233. #1383 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 306. C2×C16 | D284 | semidirect |
| 308. #108 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| #22598061 | 2 |
| #22598003 | 2 |
| C2×#17985808 | 2 |
| #22590067 | 2 |
| #22589967 | 2 |
| C71×#1383 | 2 |
| #13318 | 71 |