Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 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. C2×#17984167 | C2 | semidirect |
| 2. C2×#17984150 | C2 | semidirect |
| 3. #22578371 | C2 | semidirect |
| 4. #22578276 | C2 | semidirect |
| 17. #17984063 | C4 | semidirect |
| 18. #17984062 | C4 | semidirect |
| 21. #17984059 | C4 | semidirect |
| 24. #121×C137 | C4 | semidirect |
| 30. C4⋊#10587739 | D4 | semidirect |
| 137. C137 | #1875 | semidirect |
| 153. #121 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984167 | 2 |
| C2×#17984150 | 2 |
| #22578371 | 2 |
| #22578276 | 2 |
| #121×D137 | 2 |
| #1875 | 137 |