Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #5555 | C2 | semidirect |
| 2. D4×D12 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. #4846 | C2 | semidirect |
| 7. #4843 | C2 | semidirect |
| 8. #4736 | C2 | semidirect |
| 9. #4732 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. C4×D24 | C2 | semidirect |
| 16. C22×C3×C8 | C22 | semidirect |
| 19. #930 | C22 | semidirect |
| 20. C2×C4⋊Dic3 | C22 | semidirect |
| 22. C2×D24 | C22 | semidirect |
| 29. C4×D12 | C22 | semidirect |
| 30. #869 | C22 | semidirect |
| 31. C3×C4⋊C8 | C22 | semidirect |
| 32. C3×C22⋊C8 | C22 | semidirect |
| 33. C3×C4×C8 | C22 | semidirect |
| 36. #821 | C22 | semidirect |
| 37. #821 | C22 | semidirect |
| 38. #821 | C22 | semidirect |
| 39. #821 | C22 | semidirect |
| 40. #818 | C22 | semidirect |
| 41. #818 | C22 | semidirect |
| 51. C8×D4 | D3 | semidirect |
| 95. C22×C8 | C2×D3 | semidirect |
| 110. C4⋊C8 | C2×D3 | semidirect |
| 117. C22⋊C8 | C2×D3 | semidirect |
| 118. C4×C8 | C2×D3 | semidirect |
| 126. C3×D4 | D8 | semidirect |
| 147. D12 | #41 | semidirect |
| 232. D4 | D24 | semidirect |
| 277. C3 | #3294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5555 | 2 |
| D4×D12 | 2 |
| C3×C8×D4 | 2 |
| #5115 | 2 |
| C2×#821 | 2 |
| #4846 | 2 |
| #4843 | 2 |
| #4736 | 2 |
| #4732 | 2 |
| #4694 | 2 |
| C4×D24 | 2 |
| #3294 | 3 |