Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #16863802 | C4 | semidirect |
| 10. #16863802 | C4 | semidirect |
| 187. C67 | #9440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570762 | 2 |
| #22563314 | 2 |
| #22558835 | 2 |
| #22558721 | 2 |
| #22558102 | 2 |
| #22558101 | 2 |
| C67×#1506 | 2 |
| #9440 | 67 |