Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #16863798 | C4 | semidirect |
| 11. #16863794 | C4 | semidirect |
| 49. M32×C67 | Q8 | semidirect |
| 51. C2×C16×C67 | Q8 | semidirect |
| 131. C67 | #13291 | semidirect |
| 162. M32 | Dic134 | semidirect |
| 164. 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 |
| #22560333 | 2 |
| #22558324 | 2 |
| #22558315 | 2 |
| #22558311 | 2 |
| #22558308 | 2 |
| C67×#2110 | 2 |
| #13291 | 67 |