Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556 | C2 | semidirect |
| 3. #5093 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5051 | C2 | semidirect |
| 6. #5047 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. C4×#215 | C2 | semidirect |
| 9. D4×C3⋊C8 | C2 | semidirect |
| 10. #5002 | C2 | semidirect |
| 11. #4996 | C2 | semidirect |
| 42. #556 | D3 | semidirect |
| 245. C3 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#556 | 2 |
| #5551 | 2 |
| #5093 | 2 |
| #5087 | 2 |
| #5051 | 2 |
| #5047 | 2 |
| #5031 | 2 |
| C4×#215 | 2 |
| D4×C3⋊C8 | 2 |
| #5002 | 2 |
| #4996 | 2 |
| #3302 | 3 |