Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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, cosocle | C23×C3 | C24 |
| Fitting | C3×#379 | C2 |
| prime radical | C25×C3 | C22 |
| hypercenter | #379 | D3 |
| hypocenter | C3 | #2483 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #4953 | C2 | semidirect |
| 4. #4950 | C2 | semidirect |
| 5. #4943 | C2 | semidirect |
| 15. C2×C4⋊Dic3 | C22 | semidirect |
| 16. C3⋊#95 | C22 | semidirect |
| 17. C3⋊#95 | C22 | semidirect |
| 139. C3 | #2483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#217 | 2 |
| C3×#379 | 2 |
| #4953 | 2 |
| #4950 | 2 |
| #4943 | 2 |
| #2483 | 3 |