Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #22578445 | C2 | semidirect |
| 2. #22578331 | C2 | semidirect |
| 3. #22578317 | C2 | semidirect |
| 4. C16×#10587739 | C2 | semidirect |
| 12. Dic1096 | C4 | semidirect |
| 13. #17984032 | C4 | semidirect |
| 15. D16×C137 | C4 | semidirect |
| 49. C137 | #2178 | semidirect |
| 60. D16 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578445 | 2 |
| #22578331 | 2 |
| #22578317 | 2 |
| C16×#10587739 | 2 |
| #22577832 | 2 |
| #2178 | 137 |