Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22578099 | C2 | semidirect |
| 2. #22577805 | C2 | semidirect |
| 3. #22577728 | C2 | semidirect |
| 4. #22577717 | C2 | semidirect |
| 5. #22577704 | C2 | semidirect |
| 6. #22577656 | C2 | semidirect |
| 7. C4×D1096 | C2 | semidirect |
| 8. #22577445 | C2 | semidirect |
| 9. #436×C137 | C2 | semidirect |
| 102. C137 | #3355 | semidirect |
| 111. #436 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578099 | 2 |
| #22577805 | 2 |
| #22577728 | 2 |
| #22577717 | 2 |
| #22577704 | 2 |
| #22577656 | 2 |
| C4×D1096 | 2 |
| #22577445 | 2 |
| #436×C137 | 2 |
| #3355 | 137 |