Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #22578414 | C2 | semidirect |
| 4. #22578369 | C2 | semidirect |
| 5. #22578282 | C2 | semidirect |
| 6. #22578278 | C2 | semidirect |
| 23. #17984005 | C4 | semidirect |
| 24. #17984004 | C4 | semidirect |
| 25. #17984004 | C4 | semidirect |
| 26. #100×C137 | C4 | semidirect |
| 114. C137 | #1931 | semidirect |
| 139. #100 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578414 | 2 |
| #22578395 | 2 |
| C2×#17984150 | 2 |
| #22578369 | 2 |
| #22578282 | 2 |
| #22578278 | 2 |
| #100×D137 | 2 |
| #1931 | 137 |