Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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 |
|---|---|---|
| 3. C22×C3×C4⋊C4 | C2 | semidirect |
| 4. C22×C4⋊Dic3 | C2 | semidirect |
| 5. C22×Dic3⋊C4 | C2 | semidirect |
| 6. C2×D3×C4⋊C4 | C2 | direct (N × H) |
| 14. C22×C4×D3 | C4 | semidirect |
| 17. C2×C3×C4⋊C4 | C22 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C2×Dic3⋊C4 | C22 | semidirect |
| 20. D3×C4⋊C4 | C22 | direct (N × H) |
| 26. C22×C4⋊C4 | D3 | direct (N × H) |
| 33. C22×C3×C4 | C2×C4 | semidirect |
| 37. C22×Dic3 | C2×C4 | semidirect |
| 41. C2×C4×D3 | C2×C4 | semidirect |
| 44. C3×C4⋊C4 | C23 | semidirect |
| 45. C4⋊Dic3 | C23 | semidirect |
| 46. Dic3⋊C4 | C23 | semidirect |
| 59. C2×C4⋊C4 | C2×D3 | direct (N × H) |
| 64. C22×D3 | C4⋊C4 | direct (N × H) |
| 70. C2×C3×C4 | C22×C4 | semidirect |
| 74. C2×Dic3 | C22×C4 | semidirect |
| 78. C4×D3 | C22×C4 | semidirect |
| 93. C22×C4 | C4×D3 | semidirect |
| 98. C4⋊C4 | C22×D3 | direct (N × H) |
| 99. C22×C3 | C2×C4⋊C4 | semidirect |
| 104. C2×D3 | C2×C4⋊C4 | direct (N × H) |
| 109. C3×C4 | C23×C4 | semidirect |
| 111. Dic3 | C23×C4 | semidirect |
| 128. C2×C4 | C2×C4×D3 | semidirect |
| 131. C2×C3 | C22×C4⋊C4 | semidirect |
| 135. D3 | C22×C4⋊C4 | direct (N × H) |
| 140. C22 | D3×C4⋊C4 | direct (N × H) |
| 148. C4 | C22×C4×D3 | semidirect |
| 149. C3 | C23×C4⋊C4 | semidirect |
| 151. C2 | C2×D3×C4⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C23×C4⋊C4 | 3 |