Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
2528 conjugacy classes of subgroups; only the 1197 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 1197 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. C24×Dic3 | C2 | semidirect |
| 3. C22×#217 | C2 | semidirect |
| 4. C2×D4×Dic3 | C2 | direct (N × H) |
| 5. C22×C4⋊Dic3 | C2 | semidirect |
| 6. C22×C4×Dic3 | C2 | semidirect |
| 9. C22×C3×D4 | C4 | semidirect |
| 16. C23×Dic3 | C22 | semidirect |
| 17. C2×#217 | C22 | semidirect |
| 18. D4×Dic3 | C22 | direct (N × H) |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 20. C2×C4×Dic3 | C22 | semidirect |
| 29. C24×C3 | C2×C4 | semidirect |
| 32. C2×C3×D4 | C2×C4 | semidirect |
| 34. C22×C3×C4 | C2×C4 | semidirect |
| 39. C22×Dic3 | D4 | direct (N × H) |
| 43. C22×Dic3 | C23 | semidirect |
| 44. #217 | C23 | semidirect |
| 45. C4⋊Dic3 | C23 | semidirect |
| 46. C4×Dic3 | C23 | semidirect |
| 48. C22×D4 | Dic3 | direct (N × H) |
| 64. C23×C3 | C22×C4 | semidirect |
| 69. C3×D4 | C22×C4 | semidirect |
| 70. C2×C3×C4 | C22×C4 | semidirect |
| 75. C2×Dic3 | C2×D4 | direct (N × H) |
| 81. C24 | C2×Dic3 | semidirect |
| 84. C2×D4 | C2×Dic3 | direct (N × H) |
| 94. C22×C4 | C2×Dic3 | semidirect |
| 102. C22×C3 | C4×D4 | semidirect |
| 104. C22×C3 | C23×C4 | semidirect |
| 108. C3×C4 | C23×C4 | semidirect |
| 111. Dic3 | C22×D4 | direct (N × H) |
| 118. C23 | C22×Dic3 | semidirect |
| 121. D4 | C22×Dic3 | direct (N × H) |
| 129. C2×C4 | C22×Dic3 | semidirect |
| 132. C2×C3 | C2×C4×D4 | semidirect |
| 139. C22 | D4×Dic3 | direct (N × H) |
| 143. C22 | C23×Dic3 | semidirect |
| 148. C4 | C23×Dic3 | semidirect |
| 149. C3 | C22×C4×D4 | semidirect |
| 151. C2 | C2×D4×Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C24×Dic3 | 2 |
| C22×#217 | 2 |
| C2×D4×Dic3 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×C4×Dic3 | 2 |
| C22×C4×D4 | 3 |