Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#822 | C2 | semidirect |
| 4. #5119 | C2 | semidirect |
| 6. #4964 | C2 | semidirect |
| 7. C3×#343 | C2 | semidirect |
| 30. #343 | D3 | semidirect |
| 188. C3 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5131 | 2 |
| C2×#823 | 2 |
| C2×#822 | 2 |
| #5119 | 2 |
| C2×#809 | 2 |
| #4964 | 2 |
| C3×#343 | 2 |
| #2063 | 3 |