Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 45. #108 | Dic3 | direct (N × H) |
| 89. Dic3 | #108 | direct (N × H) |
| 118. C3 | C4×#108 | 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×C8×Dic3 | 2 |
| #4558 | 2 |
| C4×#108 | 3 |