Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22560495 | C2 | semidirect |
| 5. #22558338 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#1858 | C2 | semidirect |
| 194. #1858 | D67 | semidirect |
| 197. C67 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569267 | 2 |
| #22561851 | 2 |
| #22560627 | 2 |
| #22560495 | 2 |
| #22558338 | 2 |
| #22558331 | 2 |
| C67×#1858 | 2 |
| #12963 | 67 |