Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
382 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. #21462040 | C2 | semidirect |
| 4. #21460873 | C2 | semidirect |
| 7. C2×#14519851 | C4 | semidirect |
| 10. C22×#11758187 | C4 | semidirect |
| 12. #16840658 | C4 | semidirect |
| 120. C61 | #12617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840820 | 2 |
| #21462055 | 2 |
| #21462040 | 2 |
| #21460873 | 2 |
| #21445621 | 2 |
| #12617 | 61 |