Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22561455 | C2 | semidirect |
| 2. #22561350 | C2 | semidirect |
| 4. #22558035 | C2 | semidirect |
| 5. #22558032 | C2 | semidirect |
| 204. C67 | #7773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561455 | 2 |
| #22561350 | 2 |
| #22561345 | 2 |
| #22558035 | 2 |
| #22558032 | 2 |
| #22558030 | 2 |
| C67×#2808 | 2 |
| #7773 | 67 |