Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
444 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 21. Q8×Dic137 | C4 | semidirect |
| 22. C4×Dic274 | C4 | semidirect |
| 23. C4×Dic274 | C4 | semidirect |
| 24. #17984053 | C4 | semidirect |
| 25. #17984053 | C4 | semidirect |
| 30. C4×Q8×C137 | C4 | semidirect |
| 115. C137 | #2320 | semidirect |
| 131. C4×Q8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10587739)⋊Q8 | 2 |
| #22578354 | 2 |
| #22578352 | 2 |
| #22578348 | 2 |
| #22578347 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578339 | 2 |
| C4×Q8×D137 | 2 |
| #2320 | 137 |