Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1066 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #15198 | C7 | direct (N × H) |
| 221. C7 | #15198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1443 | 2 |
| C7×C4⋊#95 | 2 |
| C4×C7×#95 | 2 |
| #15198 | 7 |