Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
928 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 233 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×#380 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×#235 | C2 |
| hypercenter | #380 | D3 |
| hypocenter | C3 | #2339 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#893 | C2 | semidirect |
| 3. C3×#380 | C2 | semidirect |
| 4. C4×#217 | C2 | semidirect |
| 5. #4973 | C2 | semidirect |
| 6. #4956 | C2 | semidirect |
| 7. #4664 | C2 | semidirect |
| 8. D3×#95 | C2 | semidirect |
| 13. C2×#235 | C4 | semidirect |
| 34. #380 | D3 | semidirect |
| 40. C22×C3×C4 | C2×C4 | semidirect |
| 45. C2×#67 | C2×C4 | semidirect |
| 56. C2×C4×D3 | C2×C4 | semidirect |
| 58. C2×Dic6 | C2×C4 | semidirect |
| 110. C2×Dic3 | #41 | semidirect |
| 111. D12 | C22⋊C4 | semidirect |
| 133. C22×C4 | C4×D3 | semidirect |
| 223. C3 | #2339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C2×#893 | 2 |
| C3×#380 | 2 |
| C4×#217 | 2 |
| #4973 | 2 |
| #4956 | 2 |
| #4664 | 2 |
| D3×#95 | 2 |
| #2339 | 3 |