Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. #5745 | C2 | semidirect |
| 3. C2×C3×#101 | C2 | semidirect |
| 4. C2×#836 | C2 | semidirect |
| 5. #5132 | C2 | semidirect |
| 6. #4751 | C2 | semidirect |
| 7. D3×#101 | C2 | semidirect |
| 34. C2×#101 | D3 | semidirect |
| 218. C3 | #2889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| #5745 | 2 |
| C2×C3×#101 | 2 |
| C2×#836 | 2 |
| #5132 | 2 |
| #4751 | 2 |
| D3×#101 | 2 |
| #2889 | 3 |