Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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 |
|---|---|---|
| 2. C23×Dic6 | C2 | semidirect |
| 3. C22×C3×C42 | C2 | semidirect |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C2×#875 | C2 | direct (N × H) |
| 14. C22×Dic6 | C22 | semidirect |
| 15. C2×C3×C42 | C22 | semidirect |
| 16. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 17. #875 | C22 | direct (N × H) |
| 22. C22×C42 | D3 | semidirect |
| 36. C2×Dic6 | C23 | semidirect |
| 37. C3×C42 | C23 | semidirect |
| 38. (C2×D3)⋊C4 | C23 | semidirect |
| 49. C2×C42 | C2×D3 | semidirect |
| 80. C42 | C22×D3 | semidirect |
| 81. C22×C3 | #124 | semidirect |
| 106. C2×C3 | C2×#124 | semidirect |
| 113. C22 | #875 | direct (N × H) |
| 120. C3 | C22×#124 | semidirect |
| 122. C2 | C2×#875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C23×Dic6 | 2 |
| C22×C3×C42 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C2×#875 | 2 |
| C22×#124 | 3 |