Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 19. #17984021 | C4 | semidirect |
| 20. #17984021 | C4 | semidirect |
| 21. #17984020 | C4 | semidirect |
| 22. #106×C137 | C4 | semidirect |
| 88. C137 | #1922 | semidirect |
| 107. #106 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578410 | 2 |
| #22578368 | 2 |
| #22578279 | 2 |
| #22578273 | 2 |
| #22578268 | 2 |
| #22577438 | 2 |
| #1922 | 137 |