Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #22578009 | C2 | direct (N × H) |
| 2. C2×#17984085 | C2 | semidirect |
| 3. C2×#17984073 | C2 | semidirect |
| 4. C2×#17984063 | C2 | semidirect |
| 5. C2×#17984063 | C2 | semidirect |
| 6. C2×#17984050 | C2 | semidirect |
| 7. C2×#17984045 | C2 | semidirect |
| 8. C2×#125×C137 | C2 | semidirect |
| 14. #17984085 | C22 | semidirect |
| 15. #17984073 | C22 | semidirect |
| 16. #17984063 | C22 | semidirect |
| 17. #17984063 | C22 | semidirect |
| 18. #17984050 | C22 | semidirect |
| 19. #17984045 | C22 | semidirect |
| 25. #125×C137 | C22 | semidirect |
| 92. C2×C137 | #540 | semidirect |
| 97. C137 | C2×#540 | semidirect |
| 101. C2×#125 | D137 | semidirect |
| 113. #125 | C2×D137 | semidirect |
| 192. C2 | #22578009 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578009 | 2 |
| C2×#17984085 | 2 |
| C2×#17984073 | 2 |
| C2×#17984063 | 2 |
| C2×#17984050 | 2 |
| C2×#17984045 | 2 |
| C2×#125×C137 | 2 |
| C2×#540 | 137 |