Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 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×#379 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C23×#67 | C2 |
| hypercenter | #379 | D3 |
| hypocenter | C3 | #2308 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D3×C22⋊C4 | C2 | semidirect |
| 3. C3×#379 | C2 | semidirect |
| 4. #5247 | C2 | semidirect |
| 5. #4956 | C2 | semidirect |
| 6. #4943 | C2 | semidirect |
| 11. C22×#67 | C4 | semidirect |
| 14. C22×C4×D3 | C22 | semidirect |
| 16. C2×C3×C22⋊C4 | C22 | semidirect |
| 18. C2×#217 | C22 | semidirect |
| 19. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 21. C3⋊#95 | C22 | semidirect |
| 27. #379 | D3 | semidirect |
| 30. C24×C3 | C2×C4 | semidirect |
| 41. C2×#67 | C2×C4 | semidirect |
| 43. C22×Dic3 | C2×C4 | semidirect |
| 65. C2×C22⋊C4 | C2×D3 | semidirect |
| 81. C22×D3 | C22⋊C4 | semidirect |
| 100. C24 | C4×D3 | semidirect |
| 190. C3 | #2308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#67 | 2 |
| C2×D3×C22⋊C4 | 2 |
| C3×#379 | 2 |
| #5247 | 2 |
| #4956 | 2 |
| #4943 | 2 |
| #2308 | 3 |