Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
114 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 26 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. #22578300 | C2 | semidirect |
| 2. #22578271 | C2 | semidirect |
| 6. C2×D1096 | C4 | semidirect |
| 10. #106×C137 | C4 | semidirect |
| 52. C137 | #1339 | semidirect |
| 62. #106 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578300 | 2 |
| #22578271 | 2 |
| #22577657 | 2 |
| #1339 | 137 |