Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22561862 | C2 | semidirect |
| 5. #22560729 | C2 | semidirect |
| 6. #22560428 | C2 | semidirect |
| 7. C67×#1391 | C2 | semidirect |
| 201. #1391 | D67 | semidirect |
| 202. C67 | #13437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571082 | 2 |
| #22561862 | 2 |
| #22561858 | 2 |
| #22560734 | 2 |
| #22560729 | 2 |
| #22560428 | 2 |
| C67×#1391 | 2 |
| #13437 | 67 |