Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #5518 | C2 | semidirect |
| 3. C3×#405 | C2 | semidirect |
| 4. #5134 | C2 | semidirect |
| 5. #5114 | C2 | semidirect |
| 6. #4713 | C2 | semidirect |
| 7. #4710 | C2 | semidirect |
| 8. #4703 | C2 | semidirect |
| 9. #4693 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4683 | C2 | semidirect |
| 50. #405 | D3 | semidirect |
| 212. C3 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5535 | 2 |
| #5518 | 2 |
| C3×#405 | 2 |
| #5134 | 2 |
| #5114 | 2 |
| #4713 | 2 |
| #4710 | 2 |
| #4703 | 2 |
| #4693 | 2 |
| C4×#204 | 2 |
| #4683 | 2 |
| #3174 | 3 |