Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22578106 | C2 | semidirect |
| 2. #22577730 | C2 | semidirect |
| 3. #22577718 | C2 | semidirect |
| 4. #22577700 | C2 | semidirect |
| 5. #22577657 | C2 | semidirect |
| 6. C4×D1096 | C2 | semidirect |
| 7. #22577482 | C2 | semidirect |
| 8. #22577442 | C2 | semidirect |
| 9. #499×C137 | C2 | semidirect |
| 102. C137 | #3355 | semidirect |
| 105. #499 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578106 | 2 |
| #22577730 | 2 |
| #22577718 | 2 |
| #22577700 | 2 |
| #22577657 | 2 |
| C4×D1096 | 2 |
| #22577482 | 2 |
| #22577442 | 2 |
| #499×C137 | 2 |
| #3355 | 137 |