Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
396 conjugacy classes of subgroups.
The subgroup lattice has 316 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×#99 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×Q8 | C23×C29 |
| prime radical | C23×C29 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×Q8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 99. #13303 | C29 | direct (N × H) |
| 216. C29 | #13303 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2565 | 2 |
| C29×#1801 | 2 |
| C4×C29×#101 | 2 |
| C29×#1394 | 2 |
| #13303 | 29 |