Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1152 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. #22571196 | C2 | semidirect |
| 2. #22570673 | C2 | semidirect |
| 3. #22559515 | C2 | semidirect |
| 4. #22559498 | C2 | semidirect |
| 5. #22558833 | C2 | semidirect |
| 6. #22558807 | C2 | semidirect |
| 7. C2×H(3,𝔽4)×C67 | C2 | semidirect |
| 10. #16863946 | C22 | semidirect |
| 11. #16863791 | C22 | semidirect |
| 12. #16863786 | C22 | semidirect |
| 13. #16863786 | C22 | semidirect |
| 15. #16863755 | C22 | semidirect |
| 19. #16863453 | C22 | semidirect |
| 20. C4×#11761612 | C22 | semidirect |
| 21. #16863136 | C22 | semidirect |
| 22. #16863136 | C22 | semidirect |
| 42. #14524043 | C23 | semidirect |
| 43. #14524040 | C23 | semidirect |
| 51. #14523954 | C23 | semidirect |
| 52. #14523954 | C23 | semidirect |
| 207. C2×H(3,𝔽4) | D67 | semidirect |
| 214. C67 | #18992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571196 | 2 |
| #22570673 | 2 |
| #22559515 | 2 |
| #22559498 | 2 |
| #22558833 | 2 |
| #22558807 | 2 |
| C2×H(3,𝔽4)×C67 | 2 |
| #18992 | 67 |