Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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×#568 | C2 | semidirect |
| 3. #5819 | C2 | semidirect |
| 4. #5132 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 15. C2×C3×M16 | C22 | semidirect |
| 17. C2×#208 | C22 | semidirect |
| 18. #824 | C22 | semidirect |
| 19. #823 | C22 | semidirect |
| 22. #568 | D3 | semidirect |
| 58. C2×M16 | C2×D3 | semidirect |
| 148. C3 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C3×#568 | 2 |
| #5819 | 2 |
| #5132 | 2 |
| C2×#823 | 2 |
| #2888 | 3 |