Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
704 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 704 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×#382 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×D12 | C22 |
| hypercenter | #382 | D3 |
| hypocenter | C3 | #2349 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#382 | C2 | semidirect |
| 4. #4972 | C2 | semidirect |
| 5. C4×C4⋊Dic3 | C2 | semidirect |
| 6. #4668 | C2 | semidirect |
| 7. #4667 | C2 | semidirect |
| 8. D3×#95 | C2 | semidirect |
| 22. C4×D12 | C4 | semidirect |
| 32. #382 | D3 | semidirect |
| 51. C2×C4×D3 | C2×C4 | semidirect |
| 53. C3×C42 | C2×C4 | semidirect |
| 55. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 57. C4⋊Dic3 | C2×C4 | semidirect |
| 102. D12 | C4⋊C4 | semidirect |
| 128. C42 | C4×D3 | semidirect |
| 196. C3 | #2349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×C4×D12 | 2 |
| C3×#382 | 2 |
| #4972 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4668 | 2 |
| #4667 | 2 |
| D3×#95 | 2 |
| #2349 | 3 |