Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C3×#428 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #4998 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4888 | C2 | semidirect |
| 9. #4884 | C2 | semidirect |
| 10. #4868 | C2 | semidirect |
| 11. #4862 | C2 | semidirect |
| 48. #428 | D3 | semidirect |
| 247. C3 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5526 | 2 |
| #5504 | 2 |
| C3×#428 | 2 |
| #5129 | 2 |
| #5120 | 2 |
| #4998 | 2 |
| C2×#810 | 2 |
| #4888 | 2 |
| #4884 | 2 |
| #4868 | 2 |
| #4862 | 2 |
| #3097 | 3 |