Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
304 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×C3×Q16 | C4 | semidirect |
| 48. C2×Q16 | Dic3 | semidirect |
| 144. C3 | #1971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| #5229 | 2 |
| C2×#835 | 2 |
| C2×#817 | 2 |
| C2×#815 | 2 |
| #1971 | 3 |