Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C43×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C61×#330 | C4 | semidirect |
| 78. #8225 | C61 | direct (N × H) |
| 111. #330 | C4×C61 | semidirect |
| 112. C61 | #8225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#125×C61 | 2 |
| C61×#1745 | 2 |
| C2×C61×#330 | 2 |
| C61×#1295 | 2 |
| #8225 | 61 |