Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
522 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21461555 | C2 | semidirect |
| 2. C8×C22⋊#6923 | C2 | semidirect |
| 5. #21460701 | C2 | semidirect |
| 6. #21460699 | C2 | semidirect |
| 16. #16840616 | C4 | semidirect |
| 17. #16840616 | C4 | semidirect |
| 18. #16840613 | C4 | semidirect |
| 19. #16840613 | C4 | semidirect |
| 20. C2×#14519784 | C4 | semidirect |
| 27. #16839788 | C4 | semidirect |
| 29. #16839720 | C4 | semidirect |
| 30. C61×#408 | C4 | semidirect |
| 224. #408 | #6923 | semidirect |
| 239. C61 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461555 | 2 |
| C8×C22⋊#6923 | 2 |
| #21461194 | 2 |
| #21460701 | 2 |
| #21460699 | 2 |
| #21454516 | 2 |
| #8240 | 61 |