Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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. #5827 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. #5233 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. #5225 | C2 | semidirect |
| 7. C2×#835 | C2 | semidirect |
| 10. C3×2−1+4 | C4 | semidirect |
| 38. C3×#41 | C2×C4 | semidirect |
| 43. C2×C3×Q8 | C2×C4 | semidirect |
| 63. 2−1+4 | Dic3 | semidirect |
| 106. #41 | C2×Dic3 | semidirect |
| 111. C2×Q8 | C2×Dic3 | semidirect |
| 183. C3 | #2898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×2−1+4 | 2 |
| #5827 | 2 |
| C2×#948 | 2 |
| #5233 | 2 |
| #5232 | 2 |
| #5225 | 2 |
| C2×#835 | 2 |
| #2898 | 3 |