Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 127. Dic3 | #108 | semidirect |
| 165. C3 | #1950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#822 | 2 |
| #5118 | 2 |
| Dic3×M16 | 2 |
| C2×#819 | 2 |
| C2×Dic3⋊C8 | 2 |
| C3×#341 | 2 |
| #4558 | 2 |
| #1950 | 3 |