Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5643 | C2 | semidirect |
| 2. C3×#470 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 6. #5122 | C2 | semidirect |
| 7. #5048 | C2 | semidirect |
| 8. #4869 | C2 | semidirect |
| 9. #4855 | C2 | semidirect |
| 10. #4794 | C2 | semidirect |
| 11. #4788 | C2 | semidirect |
| 44. #470 | D3 | semidirect |
| 214. C3 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5643 | 2 |
| C3×#470 | 2 |
| #5191 | 2 |
| #5184 | 2 |
| #5135 | 2 |
| #5122 | 2 |
| #5048 | 2 |
| #4869 | 2 |
| #4855 | 2 |
| #4794 | 2 |
| #4788 | 2 |
| #3173 | 3 |