Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
310 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 35. #14523983 | Q8 | semidirect |
| 37. C2×C67⋊C16 | Q8 | semidirect |
| 54. #108×C67 | Q8 | semidirect |
| 133. C67 | #13460 | semidirect |
| 173. #108 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570740 | 2 |
| #22561983 | 2 |
| C2×#16863220 | 2 |
| #22558323 | 2 |
| #22558309 | 2 |
| #22558295 | 2 |
| C67×#1953 | 2 |
| #13460 | 67 |