Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22578401 | C2 | semidirect |
| 2. #22578395 | C2 | semidirect |
| 3. #22578389 | C2 | semidirect |
| 4. #22578382 | C2 | semidirect |
| 6. D137⋊M16 | C22 | semidirect |
| 7. #17984167 | C22 | semidirect |
| 16. C2×#14555510 | C4 | semidirect |
| 19. C2×#14555509 | C4 | semidirect |
| 24. C2×D4×D137 | C4 | semidirect |
| 26. C22×D4×C137 | C4 | semidirect |
| 151. C137 | #1795 | semidirect |
| 170. C22×D4 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578401 | 2 |
| #22578395 | 2 |
| #22578389 | 2 |
| #22578382 | 2 |
| C2×#17984133 | 2 |
| #1795 | 137 |