Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C2×#953 | C2 |
| hypercenter | #379 | D3 |
| hypocenter | C3 | C4×#120 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic3 | C2 | semidirect |
| 3. C2×#67⋊C4 | C2 | semidirect |
| 4. C3×#379 | C2 | semidirect |
| 5. #4958 | C2 | semidirect |
| 6. #4946 | C2 | semidirect |
| 7. Dic3×C22⋊C4 | C2 | semidirect |
| 14. C22×C4×D3 | C22 | semidirect |
| 17. #953 | C4 | semidirect |
| 19. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 20. C2×Dic3⋊C4 | C22 | semidirect |
| 21. C2×C4×Dic3 | C22 | semidirect |
| 23. C3⋊#95 | C22 | semidirect |
| 29. #379 | D3 | semidirect |
| 33. C24×C3 | C2×C4 | semidirect |
| 40. C2×#67 | C2×C4 | semidirect |
| 45. C22×Dic3 | D4 | semidirect |
| 52. #217 | C2×C4 | semidirect |
| 82. C22×D3 | C22×C4 | semidirect |
| 92. C2×Dic3 | C22×C4 | semidirect |
| 99. C24 | C4×D3 | semidirect |
| 126. C22×C3 | C4×D4 | semidirect |
| 137. Dic3 | #120 | semidirect |
| 176. C22 | #67⋊C4 | semidirect |
| 185. C3 | C4×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic3 | 2 |
| C2×#953 | 2 |
| C2×#67⋊C4 | 2 |
| C3×#379 | 2 |
| #4958 | 2 |
| #4946 | 2 |
| Dic3×C22⋊C4 | 2 |
| C4×#120 | 3 |