Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2886 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C53 | C23 |
| commutator | C23 | C2×C42×C53 |
| Frattini, cosocle | C25 | C23×C53 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C22×C4⋊C4×C53 | C4 | semidirect |
| 14. C2×#95×C53 | C4 | semidirect |
| 104. C22×C4×C53 | C4⋊C4 | semidirect |
| 167. C2×C4×C53 | #95 | semidirect |
| 168. #7557 | C53 | direct (N × H) |
| 229. C22×C4⋊C4 | C4×C53 | semidirect |
| 234. C2×#95 | C4×C53 | semidirect |
| 235. C53 | #7557 | direct (N × H) |
| 325. C22×C4 | C4⋊C4×C53 | semidirect |
| 388. C2×C4 | #95×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4×C53 | 2 |
| C22×#95×C53 | 2 |
| #7557 | 53 |