Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 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×C3×C4×C8 | C2 | semidirect |
| 4. C2×Dic3⋊C8 | C2 | semidirect |
| 5. C2×#803 | C2 | semidirect |
| 6. #4690 | C2 | direct (N × H) |
| 17. C3×C4×C8 | C22 | semidirect |
| 19. Dic3⋊C8 | C22 | semidirect |
| 20. #803 | C22 | semidirect |
| 26. C2×C4×C8 | D3 | semidirect |
| 57. C4×C8 | C2×D3 | semidirect |
| 121. C2×C3 | #433 | semidirect |
| 136. C3 | C2×#433 | semidirect |
| 138. C2 | #4690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#872 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#803 | 2 |
| #4690 | 2 |
| C2×#433 | 3 |