Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22578404 | C2 | semidirect |
| 2. C2×#17984151 | C2 | semidirect |
| 4. C4×C4⋊#10587739 | C2 | semidirect |
| 16. #17984077 | C4 | semidirect |
| 17. #17984076 | C4 | semidirect |
| 18. #17984075 | C4 | semidirect |
| 24. #124×C137 | C4 | semidirect |
| 122. C137 | #1983 | semidirect |
| 137. #124 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C2×#17984151 | 2 |
| C2×#17984150 | 2 |
| C4×C4⋊#10587739 | 2 |
| #124×D137 | 2 |
| #1983 | 137 |