Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5771 | C2 | semidirect |
| 2. #5766 | C2 | semidirect |
| 3. C3×#510 | C2 | semidirect |
| 4. #5194 | C2 | semidirect |
| 5. C2×#829 | C2 | semidirect |
| 6. #4918 | C2 | semidirect |
| 7. D3×Q32 | C2 | semidirect |
| 8. #4916 | C2 | semidirect |
| 9. #4915 | C2 | semidirect |
| 10. #4909 | C2 | semidirect |
| 11. #4907 | C2 | semidirect |
| 47. #510 | D3 | semidirect |
| 241. C3 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5771 | 2 |
| #5766 | 2 |
| C3×#510 | 2 |
| #5194 | 2 |
| C2×#829 | 2 |
| #4918 | 2 |
| D3×Q32 | 2 |
| #4916 | 2 |
| #4915 | 2 |
| #4909 | 2 |
| #4907 | 2 |
| #3417 | 3 |