Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
5796 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C3 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#585 | C2 | semidirect |
| 2. C2×C3×2−1+4 | C2 | semidirect |
| 3. 2−1+6 | C3 | direct (N × H) |
| 4. C3×2−1+4 | C22 | semidirect |
| 5. C3×H(5,𝔽2) | C22 | semidirect |
| 6. C2×C3×#41 | C22 | semidirect |
| 7. C22×C3×Q8 | C22 | semidirect |
| 8. #585 | C2×C3 | semidirect |
| 9. C2×2−1+4 | C2×C3 | semidirect |
| 14. 2−1+4 | C22×C3 | semidirect |
| 15. H(5,𝔽2) | C22×C3 | semidirect |
| 16. C2×#41 | C22×C3 | semidirect |
| 17. C22×Q8 | C22×C3 | semidirect |
| 38. C3 | 2−1+6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#585 | 2 |
| C2×C3×2−1+4 | 2 |
| 2−1+6 | 3 |