Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #22578352 | C2 | semidirect |
| 3. C4×C4⋊#10587739 | C2 | semidirect |
| 5. #22578339 | C2 | semidirect |
| 6. C42×#10587739 | C2 | semidirect |
| 17. #17984047 | C4 | semidirect |
| 18. #17984046 | C4 | semidirect |
| 19. #17984045 | C4 | semidirect |
| 20. #17984045 | C4 | semidirect |
| 21. #17984044 | C4 | semidirect |
| 26. #117×C137 | C4 | semidirect |
| 108. C137 | #2298 | semidirect |
| 123. #117 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578353 | 2 |
| #22578352 | 2 |
| C4×C4⋊#10587739 | 2 |
| C4×C22⋊#10587739 | 2 |
| #22578339 | 2 |
| C42×#10587739 | 2 |
| #117×D137 | 2 |
| #2298 | 137 |