Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. C2×C3×#107 | C2 | semidirect |
| 4. C2×#818 | C2 | semidirect |
| 5. C2×#808 | C2 | semidirect |
| 6. #4880 | C2 | direct (N × H) |
| 15. C2×D3×C8 | C4 | semidirect |
| 19. C3×#107 | C22 | semidirect |
| 20. #818 | C22 | semidirect |
| 21. #808 | C22 | semidirect |
| 26. C2×#107 | D3 | semidirect |
| 47. D3×C8 | C2×C4 | semidirect |
| 60. #107 | C2×D3 | semidirect |
| 136. C2×C3 | #427 | semidirect |
| 155. C3 | C2×#427 | semidirect |
| 157. C2 | #4880 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×#892 | 2 |
| C2×C3×#107 | 2 |
| C2×#818 | 2 |
| C2×#808 | 2 |
| #4880 | 2 |
| C2×#427 | 3 |