Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1182 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 371 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. #16839630 | C4 | semidirect |
| 48. C42×C61 | C4⋊C4 | semidirect |
| 105. C61 | #14678 | semidirect |
| 140. C42 | #11758196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839632 | 2 |
| C2×#16839630 | 2 |
| #21444083 | 2 |
| #21444075 | 2 |
| C2×C61×#383 | 2 |
| #14678 | 61 |