Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #5523 | C2 | semidirect |
| 3. C3×#428 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5129 | C2 | semidirect |
| 6. #5002 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4888 | C2 | semidirect |
| 9. #4885 | C2 | semidirect |
| 10. #4863 | C2 | semidirect |
| 11. #4862 | C2 | semidirect |
| 48. #428 | D3 | semidirect |
| 260. C3 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5523 | 2 |
| #5510 | 2 |
| C3×#428 | 2 |
| #5133 | 2 |
| #5129 | 2 |
| #5002 | 2 |
| C2×#808 | 2 |
| #4888 | 2 |
| #4885 | 2 |
| #4863 | 2 |
| #4862 | 2 |
| #3099 | 3 |