Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #5546 | C2 | semidirect |
| 3. C3×#442 | C2 | semidirect |
| 4. #5152 | C2 | semidirect |
| 5. C4×#214 | C2 | semidirect |
| 6. D3×#106 | C2 | semidirect |
| 7. #4853 | C2 | semidirect |
| 8. #4771 | C2 | semidirect |
| 9. #4758 | C2 | semidirect |
| 10. #4716 | C2 | semidirect |
| 11. #4708 | C2 | semidirect |
| 20. #912 | C4 | semidirect |
| 44. #442 | D3 | semidirect |
| 58. #237 | C2×C4 | semidirect |
| 62. C3×D8 | C2×C4 | semidirect |
| 69. #214 | C2×C4 | semidirect |
| 81. Dic12 | C2×C4 | semidirect |
| 83. D3×C8 | C2×C4 | semidirect |
| 148. D8 | C4×D3 | semidirect |
| 224. C3 | #2952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#912 | 2 |
| #5546 | 2 |
| C3×#442 | 2 |
| #5152 | 2 |
| C4×#214 | 2 |
| D3×#106 | 2 |
| #4853 | 2 |
| #4771 | 2 |
| #4758 | 2 |
| #4716 | 2 |
| #4708 | 2 |
| #2952 | 3 |