Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
516 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 17. #17984088 | C4 | semidirect |
| 18. #17984087 | C4 | semidirect |
| 19. #17984086 | C4 | semidirect |
| 22. C4⋊Q8×C137 | C4 | semidirect |
| 83. C137 | #2327 | semidirect |
| 95. C4⋊Q8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10587739 | 2 |
| (C2×#10587739)⋊Q8 | 2 |
| #22578352 | 2 |
| #22578347 | 2 |
| #22578339 | 2 |
| C4⋊Q8×D137 | 2 |
| #2327 | 137 |