Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #22578366 | C2 | semidirect |
| 4. C2×C8×#10587739 | C2 | semidirect |
| 5. #22578278 | C2 | semidirect |
| 6. #22578275 | C2 | semidirect |
| 12. #17984153 | C4 | semidirect |
| 13. #17984152 | C4 | semidirect |
| 14. #17984151 | C4 | semidirect |
| 15. #17984150 | C4 | semidirect |
| 22. #17984096 | C4 | semidirect |
| 23. #17984095 | C4 | semidirect |
| 25. #17984094 | C4 | semidirect |
| 30. #131×C137 | C4 | semidirect |
| 127. C137 | #1764 | semidirect |
| 142. #131 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#104 | 2 |
| #22578393 | 2 |
| #22578366 | 2 |
| C2×C8×#10587739 | 2 |
| #22578278 | 2 |
| #22578275 | 2 |
| #131×D137 | 2 |
| #1764 | 137 |