Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. #22578459 | C2 | semidirect |
| 2. C2×#17984157 | C2 | semidirect |
| 3. #22578316 | C2 | semidirect |
| 4. #22578315 | C2 | semidirect |
| 13. #17984111 | C4 | semidirect |
| 14. #17984110 | C4 | semidirect |
| 17. #17984107 | C4 | semidirect |
| 22. #135×C137 | C4 | semidirect |
| 37. Dic548 | C2×C4 | semidirect |
| 42. D1096 | C2×C4 | semidirect |
| 50. Q16×C137 | C2×C4 | semidirect |
| 52. D8×C137 | C2×C4 | semidirect |
| 106. C137 | #2139 | semidirect |
| 119. #135 | #10587739 | semidirect |
| 144. Q16 | C2×#10587739 | semidirect |
| 151. D8 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578459 | 2 |
| C2×#17984157 | 2 |
| #22578316 | 2 |
| #22578315 | 2 |
| #135×D137 | 2 |
| #2139 | 137 |