Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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×#492 | C2 | semidirect |
| 3. #5084 | C2 | semidirect |
| 4. #4544 | C2 | semidirect |
| 5. #4459 | C2 | semidirect |
| 9. C3×C4⋊Q8 | C22 | semidirect |
| 14. C3×C4×C8 | C22 | semidirect |
| 17. C4⋊(C3⋊C8) | C22 | semidirect |
| 19. #492 | D3 | semidirect |
| 42. C4⋊Q8 | C2×D3 | semidirect |
| 50. C4×C8 | C2×D3 | semidirect |
| 65. D12 | SD16 | semidirect |
| 134. C3 | #1629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5717 | 2 |
| C3×#492 | 2 |
| #5084 | 2 |
| #4544 | 2 |
| #4459 | 2 |
| #1629 | 3 |