Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1278 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C43×C7 | C4 | semidirect |
| 6. #14690 | C7 | direct (N × H) |
| 22. C43 | C4×C7 | semidirect |
| 52. C7 | #14690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C7 | 2 |
| C7×#1434 | 2 |
| #14690 | 7 |