Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #22578427 | C2 | semidirect |
| 2. #22578426 | C2 | semidirect |
| 3. #22578422 | C2 | semidirect |
| 4. #22578410 | C2 | semidirect |
| 7. #22578368 | C2 | semidirect |
| 11. #17984155 | C22 | semidirect |
| 12. C4⋊#11764047 | C22 | semidirect |
| 18. #17984143 | C22 | semidirect |
| 19. C4×#11764047 | C22 | semidirect |
| 110. C137 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578427 | 2 |
| #22578426 | 2 |
| #22578422 | 2 |
| #22578410 | 2 |
| #22578374 | 2 |
| #22578371 | 2 |
| #22578368 | 2 |
| #117×D137 | 2 |
| #2924 | 137 |