Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
456 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C29 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C43×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 100. #8582 | C29 | direct (N × H) |
| 226. C29 | #8582 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C29×#125 | 2 |
| C29×#1767 | 2 |
| C2×C29×#330 | 2 |
| C29×#1295 | 2 |
| #8582 | 29 |