Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
290 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 70 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×#17984156 | C2 | semidirect |
| 4. C4⋊C4×#10587739 | C2 | semidirect |
| 5. #22578276 | C2 | semidirect |
| 6. #22578268 | C2 | semidirect |
| 21. #17984010 | C4 | semidirect |
| 22. #17984009 | C4 | semidirect |
| 23. #17984008 | C4 | semidirect |
| 24. #102×C137 | C4 | semidirect |
| 134. C137 | #1926 | semidirect |
| 158. #102 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984156 | 2 |
| C2×#17984150 | 2 |
| #22578355 | 2 |
| C4⋊C4×#10587739 | 2 |
| #22578276 | 2 |
| #22578268 | 2 |
| #102×D137 | 2 |
| #1926 | 137 |