Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C3×#427 | C2 | semidirect |
| 3. #5116 | C2 | semidirect |
| 5. #4996 | C2 | semidirect |
| 6. #4887 | C2 | semidirect |
| 7. #4880 | C2 | semidirect |
| 8. #4874 | C2 | semidirect |
| 9. #4873 | C2 | semidirect |
| 10. #4868 | C2 | semidirect |
| 11. #4854 | C2 | semidirect |
| 50. #427 | D3 | semidirect |
| 223. C3 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5533 | 2 |
| C3×#427 | 2 |
| #5116 | 2 |
| C8×#67 | 2 |
| #4996 | 2 |
| #4887 | 2 |
| #4880 | 2 |
| #4874 | 2 |
| #4873 | 2 |
| #4868 | 2 |
| #4854 | 2 |
| #3342 | 3 |