Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1426 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D61 |
| commutator, socle, cosocle | C24×C61 | C24 |
| Fitting | C61×#1438 | C2 |
| prime radical | C23×D4×C61 | C22 |
| hypercenter | #1438 | D61 |
| hypocenter | C61 | #17273 |
| LCS | G ▷ C24×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21444088 | C2 | semidirect |
| 2. #21444064 | C2 | semidirect |
| 137. C61 | #17273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21444088 | 2 |
| #21444064 | 2 |
| #21444060 | 2 |
| C61×#1438 | 2 |
| #17273 | 61 |