Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #22571212 | C2 | semidirect |
| 2. #22570595 | C2 | semidirect |
| 3. #22559515 | C2 | semidirect |
| 4. #22558833 | C2 | semidirect |
| 5. #22558807 | C2 | semidirect |
| 7. #16863953 | C22 | semidirect |
| 8. #16863791 | C22 | semidirect |
| 9. #16863755 | C22 | semidirect |
| 10. #16863755 | C22 | semidirect |
| 15. #16863453 | C22 | semidirect |
| 18. C4×#11761612 | C22 | semidirect |
| 19. #16863136 | C22 | semidirect |
| 20. #16863136 | C22 | semidirect |
| 33. #14524043 | C23 | semidirect |
| 44. #14523954 | C23 | semidirect |
| 45. #14523954 | C23 | semidirect |
| 189. C67 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571212 | 2 |
| #22570595 | 2 |
| #22559515 | 2 |
| #22558833 | 2 |
| #22558807 | 2 |
| C2×H(3,𝔽4)×C67 | 2 |
| #18997 | 67 |