Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
304 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #22558382 | C2 | semidirect |
| 5. #22558377 | C2 | semidirect |
| 6. #22558377 | C2 | semidirect |
| 7. C67×#1413 | C2 | semidirect |
| 156. #1413 | D67 | semidirect |
| 159. C67 | #13612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571293 | 2 |
| #22561902 | 2 |
| #22561897 | 2 |
| #22558382 | 2 |
| #22558377 | 2 |
| C67×#1413 | 2 |
| #13612 | 67 |