Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1110 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #381 |
| commutator | C24 | C22×C4×C61 |
| Frattini, cosocle | C25 | C23×C61 |
| prime radical | C23×D4×C61 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C25×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C61×#342 | C2 | semidirect |
| 10. C61×#381 | C4 | semidirect |
| 11. C61×#379 | C4 | semidirect |
| 106. #11166 | C61 | direct (N × H) |
| 132. C2×#342 | C2×C61 | semidirect |
| 146. #381 | C4×C61 | semidirect |
| 147. #379 | C4×C61 | semidirect |
| 149. C61 | #11166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#99×C61 | 2 |
| C61×#2308 | 2 |
| C2×C61×#342 | 2 |
| #11166 | 61 |