Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. #5225 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 9. C3×C4⋊Q8 | C4 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 55. C4⋊Q8 | Dic3 | semidirect |
| 56. #124 | Dic3 | semidirect |
| 156. C3 | #1909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| #5819 | 2 |
| #5240 | 2 |
| #5225 | 2 |
| #4531 | 2 |
| #1909 | 3 |