Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 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. #22561904 | C2 | semidirect |
| 5. #22560429 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#1915 | C2 | semidirect |
| 196. #1915 | D67 | semidirect |
| 200. C67 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571076 | 2 |
| #22561904 | 2 |
| #22561900 | 2 |
| #22560756 | 2 |
| #22560429 | 2 |
| #22558331 | 2 |
| C67×#1915 | 2 |
| #13430 | 67 |