Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 9. #16840623 | C4 | semidirect |
| 11. C4⋊#11758185 | C4 | semidirect |
| 14. C61×C4⋊C16 | C4 | semidirect |
| 102. C4⋊C16 | #6923 | semidirect |
| 108. C61 | #7302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519845 | 2 |
| #21461374 | 2 |
| #21447621 | 2 |
| #7302 | 61 |