Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic3 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×#830 | C2 | semidirect |
| 5. #5033 | C2 | direct (N × H) |
| 6. C2×#807 | C2 | semidirect |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 21. #832 | C22 | semidirect |
| 22. #830 | C22 | semidirect |
| 23. #807 | C22 | semidirect |
| 163. C2×C3 | #480 | semidirect |
| 184. C3 | C2×#480 | semidirect |
| 187. C2 | #5033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×#832 | 2 |
| C2×#830 | 2 |
| #5033 | 2 |
| C2×#807 | 2 |
| C2×#480 | 3 |