Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C4×D4 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. #5477 | C2 | semidirect |
| 4. #5019 | C2 | semidirect |
| 5. #5016 | C2 | semidirect |
| 6. #5015 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 8. #4924 | C2 | semidirect |
| 26. #875 | C22 | semidirect |
| 27. #874 | C22 | semidirect |
| 30. #869 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 32. #809 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 34. C4⋊(C3⋊C8) | C22 | semidirect |
| 37. C2×C4×D4 | D3 | semidirect |
| 46. C2×C3×D4 | D4 | semidirect |
| 147. C2×D4 | D12 | semidirect |
| 189. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 249. C4 | #932 | 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×C3×C4×D4 | 2 |
| C2×#932 | 2 |
| #5477 | 2 |
| #5019 | 2 |
| #5016 | 2 |
| #5015 | 2 |
| #4966 | 2 |
| #4924 | 2 |
| #3036 | 3 |