Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 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. #4980 | C2 | semidirect |
| 3. Dic3×C4⋊C4 | C2 | semidirect |
| 6. #4937 | C2 | semidirect |
| 7. C42×Dic3 | C2 | semidirect |
| 10. C3×#126 | C4 | semidirect |
| 38. C3×C4⋊C4 | C2×C4 | semidirect |
| 40. C3×C42 | C2×C4 | semidirect |
| 47. #126 | Dic3 | direct (N × H) |
| 88. C4⋊C4 | C2×Dic3 | semidirect |
| 94. C42 | C2×Dic3 | semidirect |
| 106. Dic3 | #126 | direct (N × H) |
| 142. C3 | C4×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#126 | 2 |
| #4980 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4951 | 2 |
| Dic3×C22⋊C4 | 2 |
| #4937 | 2 |
| C42×Dic3 | 2 |
| C4×#126 | 3 |