Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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×C22⋊C8 | C2 | semidirect |
| 3. D3×#95 | C2 | semidirect |
| 4. C3×#327 | C2 | semidirect |
| 5. #4537 | C2 | semidirect |
| 6. #4470 | C2 | semidirect |
| 7. #4451 | C2 | semidirect |
| 10. C2×D3×D4 | C4 | semidirect |
| 15. #938 | C4 | semidirect |
| 18. #895 | C4 | semidirect |
| 19. D3×C4⋊C4 | C4 | semidirect |
| 22. C3×C22⋊C8 | C22 | semidirect |
| 23. C3×#95 | C22 | semidirect |
| 25. C3⋊#95 | C22 | semidirect |
| 26. #830 | C22 | semidirect |
| 34. #327 | D3 | direct (N × H) |
| 38. C2×C3×D4 | C2×C4 | semidirect |
| 50. C2×D12 | C2×C4 | semidirect |
| 61. C3×C4⋊C4 | C2×C4 | semidirect |
| 66. C4⋊Dic3 | C2×C4 | semidirect |
| 85. C22⋊C8 | C2×D3 | semidirect |
| 88. #95 | C2×D3 | semidirect |
| 143. C2×D4 | C4×D3 | semidirect |
| 162. C4⋊C4 | C4×D3 | semidirect |
| 246. D3 | #327 | direct (N × H) |
| 275. C3 | C2×#327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#121 | 2 |
| D3×C22⋊C8 | 2 |
| D3×#95 | 2 |
| C3×#327 | 2 |
| #4537 | 2 |
| #4470 | 2 |
| #4451 | 2 |
| C2×#327 | 3 |