Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 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. C22×C3×C42 | C2 | semidirect |
| 3. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C22×C4⋊Dic3 | C2 | semidirect |
| 5. #4939 | C2 | direct (N × H) |
| 13. C22×D12 | C4 | semidirect |
| 16. C2×C3×C42 | C22 | semidirect |
| 18. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 20. C2×C4⋊Dic3 | C22 | semidirect |
| 24. C22×C42 | D3 | semidirect |
| 38. C22×C3×C4 | D4 | semidirect |
| 47. C2×D12 | C2×C4 | semidirect |
| 64. C2×C42 | C2×D3 | semidirect |
| 84. C2×C3×C4 | C22⋊C4 | semidirect |
| 88. C2×C3×C4 | C2×D4 | semidirect |
| 111. C22×C4 | D12 | semidirect |
| 135. C3×C4 | C2×C22⋊C4 | semidirect |
| 160. C2×C4 | (C2×D3)⋊C4 | semidirect |
| 163. C2×C4 | C2×D12 | semidirect |
| 165. C2×C3 | #390 | semidirect |
| 190. C4 | C2×(C2×D3)⋊C4 | semidirect |
| 191. C3 | C2×#390 | semidirect |
| 193. C2 | #4939 | 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 |
| C22×C3×C42 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| #4939 | 2 |
| C2×#390 | 3 |