Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 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. C3×#376 | C2 | semidirect |
| 4. #4932 | C2 | semidirect |
| 5. C42×Dic3 | C2 | semidirect |
| 7. #4649 | C2 | semidirect |
| 19. #872 | C4 | semidirect |
| 20. C42×D3 | C4 | semidirect |
| 28. #376 | D3 | semidirect |
| 42. C3×C42 | C2×C4 | semidirect |
| 44. Dic3⋊C4 | C2×C4 | semidirect |
| 48. C4×Dic3 | C2×C4 | semidirect |
| 80. C4×D3 | C42 | semidirect |
| 99. C42 | C4×D3 | semidirect |
| 111. Dic3 | #117 | semidirect |
| 146. C3 | C4×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#872 | 2 |
| C2×C42×D3 | 2 |
| C3×#376 | 2 |
| #4932 | 2 |
| C42×Dic3 | 2 |
| #4666 | 2 |
| #4649 | 2 |
| C4×#117 | 3 |