Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
712 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 6. #4650 | C2 | direct (N × H) |
| 15. C2×C4×Dic3 | C4 | semidirect |
| 46. C4×Dic3 | C2×C4 | semidirect |
| 143. C2×C3 | #382 | semidirect |
| 164. C3 | C2×#382 | semidirect |
| 165. C2 | #4650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×C3×#95 | 2 |
| C2×C3⋊#95 | 2 |
| #4650 | 2 |
| C2×#382 | 3 |