Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
516 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #22568799 | C2 | semidirect |
| 2. #22561945 | C2 | semidirect |
| 3. C2×#16863178 | C2 | semidirect |
| 4. #22558310 | C2 | semidirect |
| 16. #470×C67 | C4 | semidirect |
| 17. #469×C67 | C4 | semidirect |
| 34. #14523975 | D4 | semidirect |
| 39. C2×Q16×C67 | C2×C4 | semidirect |
| 41. C2×D8×C67 | C2×C4 | semidirect |
| 55. #106×C67 | C2×C4 | semidirect |
| 167. C67 | #13008 | semidirect |
| 173. #470 | Dic67 | semidirect |
| 174. #469 | Dic67 | semidirect |
| 187. C2×Q16 | C2×Dic67 | semidirect |
| 189. C2×D8 | C2×Dic67 | semidirect |
| 217. #106 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568799 | 2 |
| #22561945 | 2 |
| C2×#16863178 | 2 |
| #22558310 | 2 |
| C67×#3054 | 2 |
| #13008 | 67 |