Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. C3×#368 | C2 | semidirect |
| 4. #4506 | C2 | semidirect |
| 5. #4493 | C2 | semidirect |
| 20. #368 | D3 | direct (N × H) |
| 93. D3 | #368 | direct (N × H) |
| 102. C3 | C2×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C16 | 2 |
| D3×#108 | 2 |
| C3×#368 | 2 |
| #4506 | 2 |
| #4493 | 2 |
| C2×#368 | 3 |