Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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. #4933 | C2 | semidirect |
| 7. #4652 | C2 | semidirect |
| 15. C2×Dic3⋊C4 | C4 | semidirect |
| 163. C3 | #2313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic3⋊C4 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C4×#217 | 2 |
| #4943 | 2 |
| #4942 | 2 |
| #4933 | 2 |
| #4652 | 2 |
| #2313 | 3 |