Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
452 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, prime radical, cosocle | C23×C3 | C24 |
| Fitting | C3×#384 | C2 |
| hypercenter | #384 | D3 |
| hypocenter | C3 | #2552 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 128. C3×C4 | #125 | semidirect |
| 180. C4 | #890 | semidirect |
| 181. C3 | #2552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#890 | 2 |
| C3×#384 | 2 |
| #4984 | 2 |
| #4982 | 2 |
| #4975 | 2 |
| #4972 | 2 |
| C4×C4⋊Dic3 | 2 |
| #2552 | 3 |