Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 2. #22568867 | C2 | semidirect |
| 5. #22558115 | C2 | semidirect |
| 6. #22558097 | C2 | semidirect |
| 7. C67×#1825 | C2 | semidirect |
| 16. #16863439 | C4 | semidirect |
| 17. #16863439 | C4 | semidirect |
| 19. #16863400 | C4 | semidirect |
| 20. #16863400 | C4 | semidirect |
| 225. #1825 | D67 | semidirect |
| 230. C67 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570149 | 2 |
| #22568867 | 2 |
| #22558776 | 2 |
| #22558568 | 2 |
| #22558115 | 2 |
| #22558097 | 2 |
| C67×#1825 | 2 |
| #9348 | 67 |