Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×#131 | C2 | semidirect |
| 3. #5825 | C2 | semidirect |
| 4. C2×#909 | C2 | semidirect |
| 5. #5137 | C2 | semidirect |
| 6. #5134 | C2 | semidirect |
| 7. #5121 | C2 | semidirect |
| 8. #5116 | C2 | semidirect |
| 9. #5114 | C2 | semidirect |
| 10. #5113 | C2 | semidirect |
| 11. C2×#816 | C2 | semidirect |
| 45. C2×#131 | D3 | semidirect |
| 76. C3×M16 | D4 | semidirect |
| 184. M16 | #67 | semidirect |
| 280. C3 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5833 | 2 |
| #5825 | 2 |
| C2×#909 | 2 |
| #5137 | 2 |
| #5134 | 2 |
| #5121 | 2 |
| #5116 | 2 |
| #5114 | 2 |
| #5113 | 2 |
| C2×#816 | 2 |
| #3063 | 3 |