Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 12. #16840653 | C4 | semidirect |
| 13. #16840652 | C4 | semidirect |
| 14. #16840651 | C4 | semidirect |
| 15. C4×#11758187 | C4 | semidirect |
| 18. #16839538 | C4 | semidirect |
| 19. C16×Dic61 | C4 | semidirect |
| 20. C61×#346 | C4 | semidirect |
| 111. #346 | #6923 | semidirect |
| 114. C61 | #12541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840653 | 2 |
| C2×#16840652 | 2 |
| C4×#14519852 | 2 |
| #21461475 | 2 |
| #21447412 | 2 |
| #12541 | 61 |