Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
460 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 20. #17984088 | C4 | semidirect |
| 21. #17984087 | C4 | semidirect |
| 22. #17984087 | C4 | semidirect |
| 23. #17984086 | C4 | semidirect |
| 27. C4⋊Q8×C137 | C4 | semidirect |
| 35. C4×#10587739 | Q8 | semidirect |
| 102. C137 | #2331 | semidirect |
| 116. 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 |
| #22578347 | 2 |
| C4⋊C4×#10587739 | 2 |
| #22578339 | 2 |
| C4⋊Q8×D137 | 2 |
| #2331 | 137 |