Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 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×C4×D3 | C2 | semidirect |
| 3. C22×C3×C42 | C2 | semidirect |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C22×C4⋊Dic3 | C2 | semidirect |
| 6. C2×C4×D12 | C2 | direct (N × H) |
| 13. C22×D12 | C4 | direct (N × H) |
| 16. C22×C4×D3 | C22 | semidirect |
| 17. C2×C3×C42 | C22 | semidirect |
| 18. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 20. C4×D12 | C22 | direct (N × H) |
| 26. C22×C42 | D3 | semidirect |
| 30. C23×D3 | C2×C4 | semidirect |
| 33. C22×C3×C4 | C2×C4 | semidirect |
| 34. C22×C3×C4 | D4 | semidirect |
| 40. C2×D12 | C2×C4 | direct (N × H) |
| 43. C2×C4×D3 | C23 | semidirect |
| 44. C3×C42 | C23 | semidirect |
| 45. (C2×D3)⋊C4 | C23 | semidirect |
| 46. C4⋊Dic3 | C23 | semidirect |
| 59. C2×C42 | C2×D3 | semidirect |
| 67. C22×D3 | C22×C4 | semidirect |
| 70. C2×C3×C4 | C22×C4 | semidirect |
| 71. C2×C3×C4 | C2×D4 | semidirect |
| 77. D12 | C22×C4 | direct (N × H) |
| 91. C22×C4 | C4×D3 | semidirect |
| 92. C22×C4 | D12 | direct (N × H) |
| 98. C42 | C22×D3 | semidirect |
| 99. C22×C3 | C4×D4 | semidirect |
| 107. C2×D3 | C23×C4 | semidirect |
| 109. C3×C4 | C23×C4 | semidirect |
| 110. C3×C4 | C22×D4 | semidirect |
| 126. C2×C4 | C2×C4×D3 | semidirect |
| 127. C2×C4 | C2×D12 | direct (N × H) |
| 131. C2×C3 | C2×C4×D4 | semidirect |
| 140. C22 | C4×D12 | direct (N × H) |
| 147. C4 | C22×C4×D3 | semidirect |
| 148. C4 | C22×D12 | direct (N × H) |
| 149. C3 | C22×C4×D4 | semidirect |
| 151. C2 | C2×C4×D12 | 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×C4×D3 | 2 |
| C22×C3×C42 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×C4×D12 | 2 |
| C22×C4×D4 | 3 |