Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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. D3×#125 | C2 | semidirect |
| 3. C3×#490 | C2 | semidirect |
| 4. #5071 | C2 | semidirect |
| 5. #5064 | C2 | semidirect |
| 6. #4777 | C2 | semidirect |
| 7. #4774 | C2 | semidirect |
| 8. #4766 | C2 | semidirect |
| 9. #4763 | C2 | semidirect |
| 10. #4705 | C2 | semidirect |
| 11. #4702 | C2 | semidirect |
| 49. #490 | D3 | semidirect |
| 251. C3 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5716 | 2 |
| D3×#125 | 2 |
| C3×#490 | 2 |
| #5071 | 2 |
| #5064 | 2 |
| #4777 | 2 |
| #4774 | 2 |
| #4766 | 2 |
| #4763 | 2 |
| #4705 | 2 |
| #4702 | 2 |
| #3234 | 3 |