Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3854 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C53 | C23 |
| commutator | C22 | C22×C42×C53 |
| Frattini, cosocle | C24 | C24×C53 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C53×C4⋊#95 | C2 | direct (N × H) |
| 10. C22×C4⋊C4×C53 | C4 | semidirect |
| 13. C22×C42×C53 | C4 | semidirect |
| 39. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 42. C2×C42×C53 | C2×C4 | semidirect |
| 73. C22×C4×C53 | C4⋊C4 | semidirect |
| 120. C2×C4×C53 | #95 | semidirect |
| 126. C2×C4×C53 | C2×C4⋊C4 | semidirect |
| 127. C2×C4⋊#95 | C53 | direct (N × H) |
| 154. C4×C53 | C2×#95 | semidirect |
| 158. C4⋊#95 | C2×C53 | direct (N × H) |
| 159. C2×C53 | C4⋊#95 | direct (N × H) |
| 173. C22×C4⋊C4 | C4×C53 | semidirect |
| 176. C22×C42 | C4×C53 | semidirect |
| 180. C53 | C2×C4⋊#95 | direct (N × H) |
| 203. C2×C4⋊C4 | C2×C4×C53 | semidirect |
| 206. C2×C42 | C2×C4×C53 | semidirect |
| 237. C22×C4 | C4⋊C4×C53 | semidirect |
| 284. C2×C4 | #95×C53 | semidirect |
| 290. C2×C4 | C2×C4⋊C4×C53 | semidirect |
| 317. C4 | C2×#95×C53 | semidirect |
| 318. C2 | C53×C4⋊#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4×C53 | 2 |
| C23×C42×C53 | 2 |
| C22×#95×C53 | 2 |
| C53×C4⋊#95 | 2 |
| C2×C4⋊#95 | 53 |