Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558765 | C2 | semidirect |
| 3. #22558739 | C2 | semidirect |
| 4. #22558570 | C2 | semidirect |
| 5. #22558118 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 7. C67×#2978 | C2 | semidirect |
| 9. #16863724 | C4 | semidirect |
| 11. #16863707 | C4 | semidirect |
| 14. #16863546 | C4 | semidirect |
| 16. #16863529 | C4 | semidirect |
| 227. #2978 | D67 | semidirect |
| 233. C67 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571019 | 2 |
| #22558765 | 2 |
| #22558739 | 2 |
| #22558570 | 2 |
| #22558118 | 2 |
| #22558085 | 2 |
| C67×#2978 | 2 |
| #9332 | 67 |