Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3×#541 | C2 | semidirect |
| 3. #5092 | C2 | semidirect |
| 4. #5086 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 6. #5068 | C2 | semidirect |
| 7. #5050 | C2 | semidirect |
| 9. #5031 | C2 | semidirect |
| 10. #5028 | C2 | semidirect |
| 11. #5000 | C2 | semidirect |
| 40. #541 | D3 | semidirect |
| 224. C3 | #3223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#541 | 2 |
| #5526 | 2 |
| #5092 | 2 |
| #5086 | 2 |
| #5069 | 2 |
| #5068 | 2 |
| #5050 | 2 |
| #5047 | 2 |
| #5031 | 2 |
| #5028 | 2 |
| #5000 | 2 |
| #3223 | 3 |