Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
382 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 22. #500×C67 | C4 | semidirect |
| 23. #498×C67 | C4 | semidirect |
| 24. #487×C67 | C4 | semidirect |
| 25. #487×C67 | C4 | semidirect |
| 165. C67 | #9280 | semidirect |
| 168. #500 | Dic67 | semidirect |
| 169. #498 | Dic67 | semidirect |
| 170. #487 | Dic67 | semidirect |
| 171. #487 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569304 | 2 |
| #22558721 | 2 |
| #22558682 | 2 |
| #22558071 | 2 |
| #22558037 | 2 |
| C67×#3231 | 2 |
| #9280 | 67 |