Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
64 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C3 | SO(3,𝔽7) |
| commutator, cosocle, hypocenter | SL(2,𝔽7) | C2×C3 |
| Frattini | C2 | C3×SO(3,𝔽7) |
| prime radical | C3×SL(2,𝔽7) | C2 |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10621463 | C3 | direct (N × H) |
| 58. C3 | #10621463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×SL(2,𝔽7) | 2 |
| #10621463 | 3 |
| C3×ΓL(1,𝔽8)⋊C4 | 8 |
| C3×Q32 | 21 |
| C3×Dic6 | 28 |