Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
156 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 10. C3×C4×C8 | C4 | semidirect |
| 14. C4⋊(C3⋊C8) | C4 | semidirect |
| 39. C4×C8 | Dic3 | semidirect |
| 125. C3 | #1286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#431 | 2 |
| #4936 | 2 |
| #4924 | 2 |
| #1286 | 3 |