Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
4632 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 4632 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 |
|---|---|---|
| 2. C23×C4×D3 | C2 | semidirect |
| 3. C22×C3×C22⋊C4 | C2 | semidirect |
| 4. C22×#217 | C2 | semidirect |
| 5. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×D3×C22⋊C4 | C2 | direct (N × H) |
| 10. C24×D3 | C4 | semidirect |
| 14. C23×C3×C4 | C22 | semidirect |
| 15. C23×Dic3 | C22 | semidirect |
| 17. C22×C4×D3 | C22 | semidirect |
| 18. C2×C3×C22⋊C4 | C22 | semidirect |
| 19. C2×#217 | C22 | semidirect |
| 20. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 21. D3×C22⋊C4 | C22 | direct (N × H) |
| 27. C22×C22⋊C4 | D3 | direct (N × H) |
| 29. C24×C3 | C2×C4 | semidirect |
| 36. C23×D3 | C2×C4 | semidirect |
| 37. C23×D3 | C2×C4 | semidirect |
| 43. C22×C3×C4 | C23 | semidirect |
| 45. C22×Dic3 | C23 | semidirect |
| 47. C2×C4×D3 | C23 | semidirect |
| 48. C3×C22⋊C4 | C23 | semidirect |
| 49. #217 | C23 | semidirect |
| 50. (C2×D3)⋊C4 | C23 | semidirect |
| 60. C23×C4 | C2×D3 | semidirect |
| 64. C2×C22⋊C4 | C2×D3 | direct (N × H) |
| 68. C23×C3 | C22×C4 | semidirect |
| 76. C22×D3 | C22⋊C4 | direct (N × H) |
| 78. C22×D3 | C22×C4 | semidirect |
| 79. C22×D3 | C22×C4 | semidirect |
| 84. C2×C3×C4 | C24 | semidirect |
| 86. C2×Dic3 | C24 | semidirect |
| 99. C24 | C4×D3 | semidirect |
| 107. C22×C4 | C22×D3 | semidirect |
| 110. C22⋊C4 | C22×D3 | direct (N × H) |
| 113. C22×C3 | C2×C22⋊C4 | semidirect |
| 115. C22×C3 | C23×C4 | semidirect |
| 121. C2×D3 | C2×C22⋊C4 | direct (N × H) |
| 123. C2×D3 | C23×C4 | semidirect |
| 141. C23 | C2×C4×D3 | semidirect |
| 149. C2×C4 | C23×D3 | semidirect |
| 151. C2×C3 | C22×C22⋊C4 | semidirect |
| 155. D3 | C22×C22⋊C4 | direct (N × H) |
| 165. C22 | D3×C22⋊C4 | direct (N × H) |
| 167. C22 | C22×C4×D3 | semidirect |
| 172. C3 | C23×C22⋊C4 | semidirect |
| 176. C2 | C2×D3×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D3 | 2 |
| C23×C4×D3 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C2×D3×C22⋊C4 | 2 |
| C23×C22⋊C4 | 3 |