Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2582 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C17 | C23 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C25 | C23×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C2×C17×#95 | C4 | semidirect |
| 105. #7556 | C17 | direct (N × H) |
| 218. C2×#95 | C4×C17 | semidirect |
| 256. C17 | #7556 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C17×#95 | 2 |
| #7556 | 17 |