Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
84 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C16×C113 | C22 |
| commutator | C2 | C22×C8×C113 |
| Frattini, cosocle | C8 | C23×C113 |
| socle | C2×C113 | C22×C8 |
| prime radical | #41×C113 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. M32×C113 | C2 | semidirect |
| 3. C2×C16×C113 | C2 | semidirect |
| 19. C113 | #504 | direct (N × H) |
| 20. #504 | C113 | direct (N × H) |
| 22. M32 | C2×C113 | semidirect |
| 23. C2×C16 | C2×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×C113 | 2 |
| M32×C113 | 2 |
| C2×C16×C113 | 2 |
| #504 | 113 |