Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Fitting | C17×#2840 | C2 |
| hypercenter | #2840 | D17 |
| hypocenter | C17 | #36675 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14536975 | C2 | semidirect |
| 2. #14536868 | C2 | semidirect |
| 3. #14536781 | C2 | semidirect |
| 4. #14532066 | C2 | semidirect |
| 5. #14532001 | C2 | semidirect |
| 6. #14531283 | C2 | semidirect |
| 7. C17×#2840 | C2 | semidirect |
| 8. C22×#63256 | C22 | semidirect |
| 11. C2×Q8×Dic17 | C22 | semidirect |
| 13. #11762751 | C22 | semidirect |
| 14. #11762736 | C22 | semidirect |
| 16. #11762728 | C22 | semidirect |
| 17. #11762727 | C22 | semidirect |
| 19. #11762720 | C22 | semidirect |
| 24. #11762656 | C22 | semidirect |
| 25. #11762654 | C22 | semidirect |
| 57. C24×C17 | #41 | semidirect |
| 111. #2840 | D17 | semidirect |
| 185. C17 | #36675 | semidirect |
| 189. C24 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14536975 | 2 |
| #14536868 | 2 |
| #14536781 | 2 |
| #14532066 | 2 |
| #14532001 | 2 |
| #14531283 | 2 |
| C17×#2840 | 2 |
| #36675 | 17 |