Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22578128 | C2 | semidirect |
| 4. #22577755 | C2 | semidirect |
| 5. #22577709 | C2 | semidirect |
| 7. #22577614 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 9. #22577497 | C2 | semidirect |
| 115. C137 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578128 | 2 |
| #22578123 | 2 |
| #22577756 | 2 |
| #22577755 | 2 |
| #22577709 | 2 |
| #22577624 | 2 |
| #22577614 | 2 |
| #22577527 | 2 |
| #22577497 | 2 |
| C4×#14555498 | 2 |
| #474×C137 | 2 |
| #3364 | 137 |