Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#936 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×#893 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4787 | C2 | direct (N × H) |
| 19. #936 | C22 | semidirect |
| 26. C2×#204 | C22 | semidirect |
| 28. #893 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. Dic3⋊C8 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 39. C2×#102 | D3 | semidirect |
| 95. #102 | C2×D3 | semidirect |
| 216. C2×C3 | #463 | semidirect |
| 240. C3 | C2×#463 | semidirect |
| 243. C2 | #4787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C22×#213 | 2 |
| C22×#204 | 2 |
| C2×#893 | 2 |
| C2×C3×#102 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#810 | 2 |
| #4787 | 2 |
| C2×#463 | 3 |