Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
300 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 15. #869 | C4 | semidirect |
| 39. C2×C3⋊C8 | Q8 | semidirect |
| 141. C3 | #1990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C3×#384 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4529 | 2 |
| #1990 | 3 |