Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1426 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C61 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C61 |
| prime radical | C23×D4×C61 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#1445 | C2 | semidirect |
| 2. C61×#1439 | C2 | semidirect |
| 98. #17273 | C61 | direct (N × H) |
| 118. #1445 | C2×C61 | semidirect |
| 119. #1439 | C2×C61 | semidirect |
| 137. C61 | #17273 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#1445 | 2 |
| C61×#1439 | 2 |
| C61×#1438 | 2 |
| #17273 | 61 |