Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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. #4850 | C2 | direct (N × H) |
| 40. C2×Dic6 | Q8 | semidirect |
| 87. Dic6 | C2×Q8 | semidirect |
| 144. C2×C3 | #477 | semidirect |
| 160. C3 | C2×#477 | semidirect |
| 161. C2 | #4850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×C4×Dic6 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#818 | 2 |
| C2×#816 | 2 |
| #4850 | 2 |
| C2×#477 | 3 |