Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 3. #22558824 | C2 | semidirect |
| 5. #22558109 | C2 | semidirect |
| 6. #22558090 | C2 | semidirect |
| 7. C67×#1518 | C2 | semidirect |
| 9. #16863802 | C4 | semidirect |
| 10. #16863788 | C4 | semidirect |
| 11. #16863764 | C4 | semidirect |
| 12. #16863758 | C4 | semidirect |
| 202. #1518 | D67 | semidirect |
| 206. C67 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570912 | 2 |
| #22569198 | 2 |
| #22558824 | 2 |
| #22558745 | 2 |
| #22558109 | 2 |
| #22558090 | 2 |
| C67×#1518 | 2 |
| #9431 | 67 |