Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5477 | C2 | semidirect |
| 2. C2×C4×D12 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4846 | C2 | semidirect |
| 5. #4843 | C2 | semidirect |
| 6. #4736 | C2 | semidirect |
| 7. #4732 | C2 | semidirect |
| 8. C4×D24 | C2 | semidirect |
| 20. #874 | C22 | semidirect |
| 26. C4×D12 | C22 | semidirect |
| 27. #869 | C22 | semidirect |
| 28. C3×C4⋊C8 | C22 | semidirect |
| 30. C3×C4×C8 | C22 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. #818 | C22 | semidirect |
| 41. #431 | D3 | semidirect |
| 93. C4⋊C8 | C2×D3 | semidirect |
| 97. C4×C8 | C2×D3 | semidirect |
| 106. C2×C3×C4 | D8 | semidirect |
| 122. D12 | #41 | semidirect |
| 201. C2×C4 | D24 | semidirect |
| 234. C3 | #3100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C2×C4×D12 | 2 |
| C3×#431 | 2 |
| #4846 | 2 |
| #4843 | 2 |
| #4736 | 2 |
| #4732 | 2 |
| C4×D24 | 2 |
| #3100 | 3 |