Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2582 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C25 | C22×D53 |
| commutator | C23×C53 | C2×C42 |
| Fitting | C22×#95×C53 | C2 |
| socle, prime radical, cosocle | C25×C53 | C23 |
| hypercenter | C22×#95 | D53 |
| hypocenter | C53 | #7556 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C2×#13133124 | C4 | semidirect |
| 228. C53 | #7556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133124 | 2 |
| C22×#95×C53 | 2 |
| #7556 | 53 |