Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578218 | C2 | semidirect |
| 2. #22578217 | C2 | semidirect |
| 3. #22577781 | C2 | semidirect |
| 4. #22577678 | C2 | semidirect |
| 5. #22577676 | C2 | semidirect |
| 6. #22577675 | C2 | semidirect |
| 7. #22577586 | C2 | semidirect |
| 8. #22577584 | C2 | semidirect |
| 9. #22577520 | C2 | semidirect |
| 10. #22577518 | C2 | semidirect |
| 11. #578×C137 | C2 | semidirect |
| 146. C137 | #3293 | semidirect |
| 150. #578 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578218 | 2 |
| #22578217 | 2 |
| #22577781 | 2 |
| #22577678 | 2 |
| #22577676 | 2 |
| #22577675 | 2 |
| #22577586 | 2 |
| #22577584 | 2 |
| #22577520 | 2 |
| #22577518 | 2 |
| #578×C137 | 2 |
| #3293 | 137 |