Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #4484 | C2 | direct (N × H) |
| 32. C2×Dic6 | C8 | semidirect |
| 81. Dic6 | C2×C8 | semidirect |
| 142. C2×C3 | Q8⋊C8 | semidirect |
| 160. C3 | C2×Q8⋊C8 | semidirect |
| 161. C2 | #4484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4484 | 2 |
| C2×Q8⋊C8 | 3 |