Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 12. C3×#108 | C4 | semidirect |
| 13. #819 | C4 | semidirect |
| 44. #108 | Dic3 | semidirect |
| 112. C3 | #1778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#108 | 2 |
| Dic3×M16 | 2 |
| C2×#819 | 2 |
| C2×#815 | 2 |
| #4558 | 2 |
| #1778 | 3 |