Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
310 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 37. #14523979 | Q8 | semidirect |
| 52. M32×C67 | Q8 | semidirect |
| 54. C2×C16×C67 | Q8 | semidirect |
| 133. C67 | #13460 | semidirect |
| 166. M32 | Dic134 | semidirect |
| 168. C2×C16 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570740 | 2 |
| #22561982 | 2 |
| C2×#16863219 | 2 |
| #22560999 | 2 |
| #22558324 | 2 |
| #22558308 | 2 |
| C67×#1378 | 2 |
| #13460 | 67 |