Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5479 | C2 | semidirect |
| 2. C2×#875 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4845 | C2 | semidirect |
| 5. #4844 | C2 | semidirect |
| 6. #4739 | C2 | semidirect |
| 7. #4738 | C2 | semidirect |
| 9. #4731 | C2 | semidirect |
| 10. #4697 | C2 | semidirect |
| 11. #4696 | C2 | semidirect |
| 22. C2×Dic12 | C22 | semidirect |
| 25. C2×#204 | C22 | semidirect |
| 31. #875 | C22 | semidirect |
| 32. C4×D12 | C22 | semidirect |
| 34. #870 | C22 | semidirect |
| 35. C4×Dic6 | C22 | semidirect |
| 36. C3×C4⋊C8 | C22 | semidirect |
| 39. C3×C4×C8 | C22 | semidirect |
| 42. #816 | C22 | semidirect |
| 43. #816 | C22 | semidirect |
| 54. #431 | D3 | semidirect |
| 119. C4⋊C8 | C2×D3 | semidirect |
| 126. C4×C8 | C2×D3 | semidirect |
| 280. C3 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C2×#875 | 2 |
| C3×#431 | 2 |
| #4845 | 2 |
| #4844 | 2 |
| #4739 | 2 |
| #4738 | 2 |
| #4732 | 2 |
| #4731 | 2 |
| #4697 | 2 |
| #4696 | 2 |
| #3211 | 3 |