Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22578126 | C2 | semidirect |
| 3. #22577750 | C2 | semidirect |
| 4. #22577730 | C2 | semidirect |
| 5. #22577688 | C2 | semidirect |
| 6. #22577635 | C2 | semidirect |
| 7. #22577603 | C2 | semidirect |
| 8. #22577564 | C2 | semidirect |
| 9. C8×D548 | C2 | semidirect |
| 10. #22577398 | C2 | semidirect |
| 11. C4×Q16×C137 | C2 | semidirect |
| 127. C137 | #3304 | semidirect |
| 137. C4×Q16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578126 | 2 |
| #22578075 | 2 |
| #22577750 | 2 |
| #22577730 | 2 |
| #22577688 | 2 |
| #22577635 | 2 |
| #22577603 | 2 |
| #22577564 | 2 |
| C8×D548 | 2 |
| #22577398 | 2 |
| C4×Q16×C137 | 2 |
| #3304 | 137 |