Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1022 conjugacy classes of subgroups; only the 680 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 680 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #6923 |
| commutator, hypocenter | C61 | C22×C4×C16 |
| Frattini | C2×C4 | C23×#6923 |
| Fitting | C23×C8×C61 | C4 |
| socle, prime radical | C24×C61 | C2×C8 |
| cosocle | C2×#92418 | C24 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16840648 | C2 | direct (N × H) |
| 4. C22×#11758187 | C4 | semidirect |
| 6. #16840648 | C22 | direct (N × H) |
| 12. C2×#11758187 | C2×C4 | semidirect |
| 30. C22×Dic61 | C16 | semidirect |
| 40. #11758187 | C22×C4 | semidirect |
| 49. C2×Dic61 | C2×C16 | semidirect |
| 55. C22×C61 | C4×C16 | semidirect |
| 62. Dic61 | C22×C16 | semidirect |
| 66. C2×C61 | C2×C4×C16 | semidirect |
| 77. C61 | C22×C4×C16 | semidirect |
| 120. C22 | #16840648 | direct (N × H) |
| 128. C2 | C2×#16840648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758187 | 2 |
| C2×#16840648 | 2 |
| C22×C8×Dic61 | 2 |
| C22×C4×C16 | 61 |