Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578074 | C2 | semidirect |
| 2. #22578068 | C2 | semidirect |
| 3. #22577751 | C2 | semidirect |
| 4. #22577748 | C2 | semidirect |
| 5. #22577682 | C2 | semidirect |
| 6. #22577599 | C2 | semidirect |
| 7. #22577597 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 9. #22577485 | C2 | semidirect |
| 10. C4×#14555495 | C2 | semidirect |
| 11. #474×C137 | C2 | semidirect |
| 78. Dic274 | D8 | semidirect |
| 84. D548 | #41 | semidirect |
| 131. C137 | #3358 | semidirect |
| 138. #474 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578074 | 2 |
| #22578068 | 2 |
| #22577751 | 2 |
| #22577748 | 2 |
| #22577682 | 2 |
| #22577599 | 2 |
| #22577597 | 2 |
| #22577527 | 2 |
| #22577485 | 2 |
| C4×#14555495 | 2 |
| #474×C137 | 2 |
| #3358 | 137 |