Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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 |
|---|---|---|
| 1. C24×C3×C4 | C2 | semidirect |
| 3. C22×#217 | C2 | semidirect |
| 4. C2×#929 | C2 | direct (N × H) |
| 5. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C22×Dic3⋊C4 | C2 | semidirect |
| 12. C23×C3×C4 | C22 | semidirect |
| 17. C2×#217 | C22 | semidirect |
| 18. #929 | C22 | direct (N × H) |
| 19. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 20. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C24×C4 | D3 | semidirect |
| 37. C22×C3×C4 | C23 | semidirect |
| 44. #217 | C23 | semidirect |
| 45. (C2×D3)⋊C4 | C23 | semidirect |
| 46. Dic3⋊C4 | C23 | semidirect |
| 55. C23×C4 | C2×D3 | semidirect |
| 95. C22×C4 | C22×D3 | semidirect |
| 101. C22×C3 | #123 | semidirect |
| 132. C2×C3 | C2×#123 | semidirect |
| 141. C22 | #929 | direct (N × H) |
| 149. C3 | C22×#123 | semidirect |
| 152. C2 | C2×#929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C23×#67 | 2 |
| C22×#217 | 2 |
| C2×#929 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×#123 | 3 |