Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22558882 | C2 | semidirect |
| 5. #22558880 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 185. #1303 | D67 | semidirect |
| 186. C67 | #9393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569232 | 2 |
| #22565204 | 2 |
| #22560198 | 2 |
| #22558882 | 2 |
| #22558880 | 2 |
| #22558112 | 2 |
| C67×#1303 | 2 |
| #9393 | 67 |