Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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. C3×C43 | C2 | semidirect |
| 5. #4937 | C2 | semidirect |
| 6. #4933 | C2 | semidirect |
| 7. C4×Dic3⋊C4 | C2 | semidirect |
| 18. #876 | C4 | direct (N × H) |
| 29. C43 | D3 | semidirect |
| 40. C3×C42 | C2×C4 | semidirect |
| 44. Dic3⋊C4 | C2×C4 | semidirect |
| 94. C42 | C4×D3 | semidirect |
| 103. C3×C4 | #126 | semidirect |
| 141. C4 | #876 | 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×#876 | 2 |
| C3×C43 | 2 |
| #4940 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4937 | 2 |
| #4933 | 2 |
| C4×Dic3⋊C4 | 2 |
| C4×#126 | 3 |