Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 2. #5812 | C2 | semidirect |
| 4. C2×#836 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 9. C3×C4⋊Q8 | C4 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 53. C4⋊Q8 | Dic3 | semidirect |
| 54. #124 | Dic3 | semidirect |
| 157. C3 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| #5812 | 2 |
| #5236 | 2 |
| C2×#836 | 2 |
| #4531 | 2 |
| #1912 | 3 |