Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#918 | C2 | semidirect |
| 3. C2×D3×Q16 | C2 | semidirect |
| 4. #5724 | C2 | semidirect |
| 5. C3×#494 | C2 | semidirect |
| 6. #5191 | C2 | semidirect |
| 7. #5190 | C2 | semidirect |
| 8. #5183 | C2 | semidirect |
| 9. #5086 | C2 | semidirect |
| 10. #4696 | C2 | semidirect |
| 11. #4689 | C2 | semidirect |
| 50. #494 | D3 | semidirect |
| 238. C3 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×#918 | 2 |
| C2×D3×Q16 | 2 |
| #5724 | 2 |
| C3×#494 | 2 |
| #5191 | 2 |
| #5190 | 2 |
| #5183 | 2 |
| #5086 | 2 |
| #4696 | 2 |
| #4689 | 2 |
| #3156 | 3 |