Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21447608 | C2 | semidirect |
| 4. #21443924 | C2 | semidirect |
| 12. #16839544 | C4 | semidirect |
| 24. #14519717 | C2×C4 | semidirect |
| 163. C61 | #12923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447608 | 2 |
| C2×#16839544 | 2 |
| #21445852 | 2 |
| #21443924 | 2 |
| C61×#2911 | 2 |
| #12923 | 61 |