Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 11. #16840624 | C4 | semidirect |
| 12. C8×#92420 | C4 | semidirect |
| 90. #92420 | #106 | semidirect |
| 92. #92418 | #97 | semidirect |
| 131. C61 | #8283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461615 | 2 |
| C2×#16840624 | 2 |
| C2×C8×#92420 | 2 |
| #21460655 | 2 |
| #21445707 | 2 |
| #8283 | 61 |