Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561187 | C2 | semidirect |
| 5. #22558099 | C2 | semidirect |
| 6. #22558041 | C2 | semidirect |
| 7. C67×#1485 | C2 | semidirect |
| 10. #16863678 | C4 | semidirect |
| 11. #16863673 | C4 | semidirect |
| 12. #16863603 | C4 | semidirect |
| 13. #16863598 | C4 | semidirect |
| 210. #1485 | D67 | semidirect |
| 213. C67 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570274 | 2 |
| #22569338 | 2 |
| #22561187 | 2 |
| C4×#14523969 | 2 |
| #22558099 | 2 |
| #22558041 | 2 |
| C67×#1485 | 2 |
| #8972 | 67 |