Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×#376 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×D12 | C22 |
| hypercenter | #376 | D3 |
| hypocenter | C3 | #2326 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×Dic6 | C2 | semidirect |
| 4. C3×#376 | C2 | semidirect |
| 6. #4935 | C2 | semidirect |
| 7. #4929 | C2 | semidirect |
| 8. #4670 | C2 | semidirect |
| 9. #4668 | C2 | semidirect |
| 25. #875 | C4 | semidirect |
| 39. #376 | D3 | semidirect |
| 56. C2×Dic6 | C2×C4 | semidirect |
| 58. C3×C42 | C2×C4 | semidirect |
| 62. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 143. C42 | C4×D3 | semidirect |
| 216. C3 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C2×C4×D12 | 2 |
| C2×C4×Dic6 | 2 |
| C3×#376 | 2 |
| #4939 | 2 |
| #4935 | 2 |
| #4929 | 2 |
| #4670 | 2 |
| #4668 | 2 |
| #2326 | 3 |