Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22563314 | C2 | semidirect |
| 3. #22558835 | C2 | semidirect |
| 5. #22558102 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 9. #16863764 | C4 | semidirect |
| 10. #16863760 | C4 | semidirect |
| 197. C67 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570609 | 2 |
| #22563314 | 2 |
| #22558835 | 2 |
| #22558717 | 2 |
| #22558102 | 2 |
| #22558101 | 2 |
| C67×#1505 | 2 |
| #9442 | 67 |