Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
696 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 4. Dic3×C4⋊C4 | C2 | semidirect |
| 8. C2×C3×C4⋊C4 | C4 | semidirect |
| 11. #926 | C4 | semidirect |
| 30. C4⋊Dic3 | C2×C4 | semidirect |
| 32. C4×Dic3 | C2×C4 | semidirect |
| 37. C2×C4⋊C4 | Dic3 | semidirect |
| 50. C2×C3×C4 | C42 | semidirect |
| 92. C2×C4 | C4×Dic3 | semidirect |
| 113. C3 | #2274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C2×#926 | 2 |
| C4×#217 | 2 |
| Dic3×C4⋊C4 | 2 |
| #2274 | 3 |