Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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. D3×Q32 | C2 | semidirect |
| 3. C3×SD64 | C2 | semidirect |
| 4. #4521 | C2 | semidirect |
| 5. #4520 | C2 | semidirect |
| 6. #4449 | C2 | semidirect |
| 7. D3×C32 | C2 | semidirect |
| 11. C3×Q32 | C22 | semidirect |
| 15. Dic24 | C22 | semidirect |
| 18. C3×C32 | C22 | semidirect |
| 19. C3⋊C32 | C22 | semidirect |
| 25. SD64 | D3 | direct (N × H) |
| 42. Q32 | C2×D3 | semidirect |
| 48. C32 | C2×D3 | semidirect |
| 93. D3 | SD64 | direct (N × H) |
| 102. C3 | C2×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q32 | 2 |
| D3×D16 | 2 |
| C3×SD64 | 2 |
| #4521 | 2 |
| #4520 | 2 |
| #4449 | 2 |
| D3×C32 | 2 |
| C2×SD64 | 3 |