Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578073 | C2 | semidirect |
| 2. D4×Dic274 | C2 | semidirect |
| 3. #22577749 | C2 | semidirect |
| 4. #22577748 | C2 | semidirect |
| 5. #22577684 | C2 | semidirect |
| 6. #22577681 | C2 | semidirect |
| 7. #22577596 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 9. D8×Dic137 | C2 | semidirect |
| 10. C4×#14555495 | C2 | semidirect |
| 11. #459×C137 | C2 | semidirect |
| 78. Dic274 | D8 | semidirect |
| 99. D4×C137 | #41 | semidirect |
| 131. C137 | #3358 | semidirect |
| 140. #459 | D137 | semidirect |
| 222. D4 | #14555509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578073 | 2 |
| D4×Dic274 | 2 |
| #22577749 | 2 |
| #22577748 | 2 |
| #22577684 | 2 |
| #22577681 | 2 |
| #22577596 | 2 |
| #22577527 | 2 |
| D8×Dic137 | 2 |
| C4×#14555495 | 2 |
| #459×C137 | 2 |
| #3358 | 137 |