Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #5184 | C2 | semidirect |
| 4. #5183 | C2 | semidirect |
| 8. #4855 | C2 | semidirect |
| 9. #4853 | C2 | semidirect |
| 10. #4792 | C2 | semidirect |
| 11. #4789 | C2 | semidirect |
| 207. C3 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5622 | 2 |
| C3×#470 | 2 |
| #5184 | 2 |
| #5183 | 2 |
| #5137 | 2 |
| Dic3×M16 | 2 |
| #5052 | 2 |
| #4855 | 2 |
| #4853 | 2 |
| #4792 | 2 |
| #4789 | 2 |
| #3185 | 3 |