Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 12. #17984022 | C4 | semidirect |
| 13. #17984022 | C4 | semidirect |
| 14. #17984020 | C4 | semidirect |
| 15. #17984020 | C4 | semidirect |
| 88. C137 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577441 | 2 |
| #22577431 | 2 |
| #22577361 | 2 |
| #22577164 | 2 |
| #22577157 | 2 |
| #341×C137 | 2 |
| #1922 | 137 |