Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
514 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. #22562482 | C2 | semidirect |
| 4. #22562461 | C2 | semidirect |
| 5. #22562437 | C2 | semidirect |
| 7. #22562065 | C2 | semidirect |
| 9. C67×#2241 | C2 | semidirect |
| 130. C4×D67 | Q32 | semidirect |
| 163. #2241 | D67 | semidirect |
| 167. C67 | #33734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570796 | 2 |
| #22570793 | 2 |
| #22562482 | 2 |
| #22562461 | 2 |
| #22562437 | 2 |
| #22562299 | 2 |
| #22562065 | 2 |
| C4×C16×D67 | 2 |
| C67×#2241 | 2 |
| #33734 | 67 |