Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D12 | C2 | semidirect |
| 3. C3×#432 | C2 | semidirect |
| 4. #4847 | C2 | semidirect |
| 5. #4844 | C2 | semidirect |
| 6. #4736 | C2 | semidirect |
| 8. #4731 | C2 | semidirect |
| 9. #4721 | C2 | semidirect |
| 10. #4711 | C2 | semidirect |
| 11. #4710 | C2 | semidirect |
| 25. #875 | C22 | semidirect |
| 30. C4×D12 | C22 | semidirect |
| 32. #870 | C22 | semidirect |
| 33. C4×Dic6 | C22 | semidirect |
| 34. C3×C4⋊C8 | C22 | semidirect |
| 37. C3×#97 | C22 | semidirect |
| 40. #821 | C22 | semidirect |
| 41. #818 | C22 | semidirect |
| 42. #817 | C22 | semidirect |
| 43. #816 | C22 | semidirect |
| 54. #432 | D3 | semidirect |
| 117. C4⋊C8 | C2×D3 | semidirect |
| 124. #97 | C2×D3 | semidirect |
| 274. C3 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C2×C4×D12 | 2 |
| C3×#432 | 2 |
| #4847 | 2 |
| #4844 | 2 |
| #4736 | 2 |
| #4732 | 2 |
| #4731 | 2 |
| #4721 | 2 |
| #4711 | 2 |
| #4710 | 2 |
| #3114 | 3 |