Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 9. C3×C4×C8 | C4 | semidirect |
| 14. C4×C3⋊C8 | C4 | semidirect |
| 28. C4×Dic3 | C8 | semidirect |
| 37. C4×C8 | Dic3 | semidirect |
| 112. C3 | #1274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#431 | 2 |
| #4932 | 2 |
| #4925 | 2 |
| #1274 | 3 |