Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. D3×M32 | C2 | semidirect |
| 3. D3×#106 | C2 | semidirect |
| 4. C3×#360 | C2 | semidirect |
| 5. #4566 | C2 | semidirect |
| 6. #4518 | C2 | semidirect |
| 7. #4488 | C2 | semidirect |
| 12. #919 | C4 | semidirect |
| 13. D3×Q16 | C4 | semidirect |
| 16. #912 | C4 | semidirect |
| 17. D3×D8 | C4 | semidirect |
| 21. C3×M32 | C22 | semidirect |
| 22. C3×#106 | C22 | semidirect |
| 23. #817 | C22 | semidirect |
| 24. #812 | C22 | semidirect |
| 34. #360 | D3 | direct (N × H) |
| 47. C3×Q16 | C2×C4 | semidirect |
| 49. C3×D8 | C2×C4 | semidirect |
| 59. Dic12 | C2×C4 | semidirect |
| 60. D24 | C2×C4 | semidirect |
| 82. M32 | C2×D3 | semidirect |
| 86. #106 | C2×D3 | semidirect |
| 131. Q16 | C4×D3 | semidirect |
| 138. D8 | C4×D3 | semidirect |
| 200. D3 | #360 | direct (N × H) |
| 216. C3 | C2×#360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#135 | 2 |
| D3×M32 | 2 |
| D3×#106 | 2 |
| C3×#360 | 2 |
| #4566 | 2 |
| #4518 | 2 |
| #4488 | 2 |
| C2×#360 | 3 |