Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
5990 conjugacy classes of subgroups; only the 504 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 504 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6923 |
| commutator, socle | C23×C61 | C23×C4 |
| Fitting, prime radical | C26×C61 | C4 |
| cosocle | C22×Dic61 | C24 |
| hypercenter | C26 | #6923 |
| hypocenter | C61 | #20579 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16840732 | C2 | semidirect |
| 2. #21461641 | C2 | semidirect |
| 4. C22×#11758217 | C22 | semidirect |
| 6. C2×C22⋊#92420 | C22 | semidirect |
| 14. C22×#92420 | C23 | semidirect |
| 39. C24×C61 | M16 | semidirect |
| 92. C22×C61 | #407 | semidirect |
| 114. C61 | #20579 | semidirect |
| 140. C24 | #11758217 | semidirect |
| 193. C22 | #16840732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840732 | 2 |
| #21461641 | 2 |
| C25×Dic61 | 2 |
| #20579 | 61 |