Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D12 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#423 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #423 | D3 |
| hypocenter | C3 | #3036 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#908 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×C4×D12 | C2 | semidirect |
| 4. C3×#423 | C2 | semidirect |
| 5. #5133 | C2 | semidirect |
| 6. #4844 | C2 | semidirect |
| 7. #4843 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 22. #875 | C22 | semidirect |
| 23. #874 | C22 | semidirect |
| 30. #869 | C22 | semidirect |
| 31. C3×C4⋊C8 | C22 | semidirect |
| 32. C3×C4⋊C8 | C22 | semidirect |
| 33. #821 | C22 | semidirect |
| 34. #816 | C22 | semidirect |
| 41. #423 | D3 | semidirect |
| 55. C2×D12 | D4 | semidirect |
| 100. C4⋊C8 | C2×D3 | semidirect |
| 101. C4⋊C8 | C2×D3 | semidirect |
| 188. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 249. C4 | #908 | semidirect |
| 252. C3 | #3036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#908 | 2 |
| #5477 | 2 |
| C2×C4×D12 | 2 |
| C3×#423 | 2 |
| #5133 | 2 |
| #4844 | 2 |
| #4843 | 2 |
| #4841 | 2 |
| #3036 | 3 |