Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
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×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C61×#2840 | C2 |
| hypercenter | #2840 | D61 |
| hypocenter | C61 | #36675 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21454010 | C2 | semidirect |
| 2. #21453903 | C2 | semidirect |
| 3. #21453816 | C2 | semidirect |
| 4. #21449101 | C2 | semidirect |
| 5. #21449036 | C2 | semidirect |
| 6. #21448318 | C2 | semidirect |
| 7. C61×#2840 | C2 | semidirect |
| 8. C22×#11758226 | C22 | semidirect |
| 11. C2×Q8×Dic61 | C22 | semidirect |
| 13. #16839704 | C22 | semidirect |
| 14. #16839689 | C22 | semidirect |
| 16. #16839681 | C22 | semidirect |
| 17. #16839680 | C22 | semidirect |
| 19. #16839673 | C22 | semidirect |
| 24. #16839609 | C22 | semidirect |
| 25. #16839607 | C22 | semidirect |
| 57. C24×C61 | #41 | semidirect |
| 126. #2840 | D61 | semidirect |
| 159. C61 | #36675 | semidirect |
| 189. C24 | #11758226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454010 | 2 |
| #21453903 | 2 |
| #21453816 | 2 |
| #21449101 | 2 |
| #21449036 | 2 |
| #21448318 | 2 |
| C61×#2840 | 2 |
| #36675 | 61 |