Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 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. C2×Q8×Dic3 | C2 | semidirect |
| 4. #5229 | C2 | semidirect |
| 6. #4951 | C2 | semidirect |
| 7. Dic3×C22⋊C4 | C2 | semidirect |
| 8. #4936 | C2 | semidirect |
| 9. C42×Dic3 | C2 | semidirect |
| 14. C3×#124 | C4 | semidirect |
| 43. C2×C3×Q8 | C2×C4 | semidirect |
| 57. C3×C22⋊C4 | C2×C4 | semidirect |
| 58. C3×C42 | C2×C4 | semidirect |
| 72. #124 | Dic3 | direct (N × H) |
| 121. C2×Q8 | C2×Dic3 | semidirect |
| 140. C22⋊C4 | C2×Dic3 | semidirect |
| 146. C42 | C2×Dic3 | semidirect |
| 164. Dic3 | #124 | direct (N × H) |
| 218. C3 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| C2×Q8×Dic3 | 2 |
| C2×D4×Dic3 | 2 |
| #5229 | 2 |
| #5221 | 2 |
| #4951 | 2 |
| Dic3×C22⋊C4 | 2 |
| #4936 | 2 |
| C42×Dic3 | 2 |
| C4×#124 | 3 |