Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
2638 conjugacy classes of subgroups.
The subgroup lattice has 304 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C29 | C23 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C24 | C24×C29 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#1443 | C2 | direct (N × H) |
| 10. C2×C29×#95 | C4 | semidirect |
| 37. C29×#95 | C2×C4 | semidirect |
| 80. C2×#1443 | C29 | direct (N × H) |
| 124. #1443 | C2×C29 | direct (N × H) |
| 153. C2×#95 | C4×C29 | semidirect |
| 157. C2×C29 | #1443 | direct (N × H) |
| 188. #95 | C2×C4×C29 | semidirect |
| 189. C29 | C2×#1443 | direct (N × H) |
| 295. C2 | C29×#1443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×#95 | 2 |
| C29×#1443 | 2 |
| C2×#1443 | 29 |