Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1114 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 340 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. #21462786 | C2 | semidirect |
| 2. C2×#16840820 | C2 | semidirect |
| 3. #21462063 | C2 | semidirect |
| 4. C2×#16840661 | C2 | semidirect |
| 8. C2×#14519851 | C22 | semidirect |
| 9. C2×#14519851 | C22 | semidirect |
| 10. C22×#11758187 | C22 | semidirect |
| 11. #16840661 | C22 | semidirect |
| 12. #16840661 | C22 | semidirect |
| 134. C61 | #33340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462786 | 2 |
| C2×#16840820 | 2 |
| #21462063 | 2 |
| C2×#16840661 | 2 |
| #21460532 | 2 |
| #33340 | 61 |