Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
650 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 650 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. #22561863 | C2 | semidirect |
| 5. #22558339 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#2135 | C2 | semidirect |
| 9. C2×#14524074 | C4 | semidirect |
| 10. C22×#11761615 | C4 | semidirect |
| 18. #16863400 | C4 | semidirect |
| 19. #16863390 | C4 | semidirect |
| 251. #2135 | D67 | semidirect |
| 256. C67 | #13097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569484 | 2 |
| #22568686 | 2 |
| #22561863 | 2 |
| #22560180 | 2 |
| #22558339 | 2 |
| #22558331 | 2 |
| C67×#2135 | 2 |
| #13097 | 67 |