Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 2. #22568689 | C2 | semidirect |
| 3. #22560758 | C2 | semidirect |
| 4. #22560624 | C2 | semidirect |
| 5. #22560321 | C2 | semidirect |
| 6. #22560133 | C2 | semidirect |
| 7. C67×#1784 | C2 | semidirect |
| 195. #1784 | D67 | semidirect |
| 196. C67 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573860 | 2 |
| #22568689 | 2 |
| #22560758 | 2 |
| #22560624 | 2 |
| #22560321 | 2 |
| #22560133 | 2 |
| C67×#1784 | 2 |
| #21780 | 67 |