Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #5728 | C2 | semidirect |
| 3. C3×#477 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 6. #4891 | C2 | semidirect |
| 7. #4880 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. D3×C4⋊C8 | C2 | semidirect |
| 11. #4796 | C2 | semidirect |
| 48. #477 | D3 | semidirect |
| 58. #239 | Q8 | semidirect |
| 263. C3 | #3076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×#239 | 2 |
| C3×#477 | 2 |
| #5084 | 2 |
| #5020 | 2 |
| #4891 | 2 |
| #4880 | 2 |
| #4846 | 2 |
| D3×C4⋊C8 | 2 |
| #4804 | 2 |
| #4796 | 2 |
| #3076 | 3 |