Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
890 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3 |
| prime radical | C23×C3 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#564 | C2 | semidirect |
| 2. C3×#557 | C2 | semidirect |
| 5. #3556 | C3 | direct (N × H) |
| 17. #564 | C2×C3 | semidirect |
| 18. #557 | C2×C3 | semidirect |
| 78. C3 | #3556 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#564 | 2 |
| C3×#557 | 2 |
| C3×#541 | 2 |
| C3×#533 | 2 |
| #3556 | 3 |