Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
524 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 197 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×#376 | C2 | semidirect |
| 4. C4×Dic3⋊C4 | C2 | semidirect |
| 5. C42×Dic3 | C2 | semidirect |
| 7. #4652 | C2 | semidirect |
| 19. #872 | C4 | semidirect |
| 28. #376 | D3 | semidirect |
| 146. C3 | #2298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#872 | 2 |
| C3×#376 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| C4×Dic3⋊C4 | 2 |
| C42×Dic3 | 2 |
| #4669 | 2 |
| #4652 | 2 |
| #2298 | 3 |