Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22570741 | C2 | semidirect |
| 4. #22558315 | C2 | semidirect |
| 5. #22558310 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 52. C2×Q16×C67 | Q8 | semidirect |
| 54. C2×D8×C67 | Q8 | semidirect |
| 164. C67 | #13374 | semidirect |
| 187. C2×Q16 | Dic134 | semidirect |
| 189. C2×D8 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570741 | 2 |
| C2×#16863206 | 2 |
| #22561108 | 2 |
| #22558315 | 2 |
| #22558310 | 2 |
| #22558294 | 2 |
| C67×#2145 | 2 |
| #13374 | 67 |