Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×#887 | C2 | semidirect |
| 3. C3×#480 | C2 | semidirect |
| 4. #5040 | C2 | semidirect |
| 5. #4967 | C2 | semidirect |
| 6. #4889 | C2 | semidirect |
| 7. #4875 | C2 | semidirect |
| 8. #4762 | C2 | semidirect |
| 9. #4757 | C2 | semidirect |
| 10. #4738 | C2 | semidirect |
| 11. #4719 | C2 | semidirect |
| 47. #480 | D3 | semidirect |
| 154. Dic6 | #41 | semidirect |
| 274. C3 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5596 | 2 |
| C2×#887 | 2 |
| C3×#480 | 2 |
| #5040 | 2 |
| #4967 | 2 |
| #4889 | 2 |
| #4875 | 2 |
| #4762 | 2 |
| #4757 | 2 |
| #4738 | 2 |
| #4719 | 2 |
| #3112 | 3 |