Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
604 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| socle | C2×C7 | C2×#401 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #23847 | C7 | direct (N × H) |
| 59. C7 | #23847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2104 | 2 |
| C7×#1740 | 2 |
| #23847 | 7 |