Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #5120 | C2 | semidirect |
| 5. #5004 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 20. #875 | C4 | semidirect |
| 31. #339 | D3 | semidirect |
| 48. C2×Dic6 | C2×C4 | semidirect |
| 56. C3×C42 | C2×C4 | semidirect |
| 142. C42 | C4×D3 | semidirect |
| 209. C3 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5521 | 2 |
| C2×#875 | 2 |
| C2×#823 | 2 |
| #5120 | 2 |
| #5004 | 2 |
| C3×#339 | 2 |
| #4523 | 2 |
| #1885 | 3 |