Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 2. #22569314 | C2 | semidirect |
| 3. #22558761 | C2 | semidirect |
| 5. #22558080 | C2 | semidirect |
| 6. #22558075 | C2 | semidirect |
| 9. #16863799 | C4 | semidirect |
| 10. #16863768 | C4 | semidirect |
| 11. #16863748 | C4 | semidirect |
| 12. #16863742 | C4 | semidirect |
| 163. C67 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570923 | 2 |
| #22569314 | 2 |
| #22558761 | 2 |
| #22558756 | 2 |
| #22558080 | 2 |
| #22558075 | 2 |
| C67×#1536 | 2 |
| #9418 | 67 |