Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C22×C3 | C23×C4 |
| Fitting | C3×#384 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C23×D3 | C23 |
| hypercenter | #384 | D3 |
| hypocenter | C3 | #2317 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C3×#384 | C2 | semidirect |
| 6. #4977 | C2 | semidirect |
| 7. #4976 | C2 | semidirect |
| 8. #4975 | C2 | semidirect |
| 9. #4936 | C2 | semidirect |
| 28. #872 | C4 | semidirect |
| 37. #384 | D3 | semidirect |
| 57. C3×C42 | C2×C4 | semidirect |
| 64. Dic3⋊C4 | C2×C4 | semidirect |
| 66. C4×Dic3 | C2×C4 | semidirect |
| 114. C4×D3 | C4⋊C4 | semidirect |
| 141. C42 | C4×D3 | semidirect |
| 212. C3 | #2317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#892 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×#872 | 2 |
| C3×#384 | 2 |
| #4989 | 2 |
| #4977 | 2 |
| #4976 | 2 |
| #4975 | 2 |
| #4936 | 2 |
| #2317 | 3 |