Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5727 | C2 | semidirect |
| 2. #5585 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. C4×#215 | C2 | semidirect |
| 6. #4870 | C2 | semidirect |
| 7. #4869 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 10. #4819 | C2 | semidirect |
| 11. #4794 | C2 | semidirect |
| 47. #475 | D3 | semidirect |
| 243. C3 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| #5585 | 2 |
| C3×#475 | 2 |
| #5088 | 2 |
| C4×#215 | 2 |
| #4870 | 2 |
| #4869 | 2 |
| #4843 | 2 |
| #4831 | 2 |
| #4819 | 2 |
| #4794 | 2 |
| #3373 | 3 |