Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1144 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 269 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×#381 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C24×D3 | C22 |
| hypercenter | #381 | D3 |
| hypocenter | C3 | C2×#381 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#381 | C2 | semidirect |
| 4. #5211 | C2 | semidirect |
| 5. #4943 | C2 | semidirect |
| 6. #4664 | C2 | semidirect |
| 7. D3×#95 | C2 | semidirect |
| 13. C22×C4×D3 | C4 | semidirect |
| 21. C3×#95 | C22 | semidirect |
| 22. C3⋊#95 | C22 | semidirect |
| 23. C3⋊#95 | C22 | semidirect |
| 29. #381 | D3 | direct (N × H) |
| 38. C22×C3×C4 | C2×C4 | semidirect |
| 42. C22×Dic3 | C2×C4 | semidirect |
| 51. C2×C4×D3 | C2×C4 | semidirect |
| 69. #95 | C2×D3 | semidirect |
| 114. C22×C4 | C4×D3 | semidirect |
| 168. D3 | #381 | direct (N × H) |
| 186. C3 | C2×#381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C2×D3×C22⋊C4 | 2 |
| C3×#381 | 2 |
| #5211 | 2 |
| #4943 | 2 |
| #4664 | 2 |
| D3×#95 | 2 |
| C2×#381 | 3 |