Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#16863219 | C2 | semidirect |
| 4. #22560963 | C2 | semidirect |
| 5. #22558314 | C2 | semidirect |
| 6. #22558288 | C2 | semidirect |
| 23. #357×C67 | C4 | semidirect |
| 54. C2×C16×C67 | C2×C4 | semidirect |
| 55. #107×C67 | C2×C4 | semidirect |
| 152. C67 | #12956 | semidirect |
| 167. #357 | Dic67 | semidirect |
| 191. C2×C16 | C2×Dic67 | semidirect |
| 194. #107 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863508 | 2 |
| C2×#16863219 | 2 |
| C2×#16863209 | 2 |
| #22560963 | 2 |
| #22558314 | 2 |
| #22558288 | 2 |
| C67×#2140 | 2 |
| #12956 | 67 |