Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 3. C22×Dic12 | C2 | semidirect |
| 4. #5143 | C2 | direct (N × H) |
| 5. C2×#824 | C2 | semidirect |
| 6. C2×#819 | C2 | semidirect |
| 24. C2×Dic12 | C22 | semidirect |
| 25. #824 | C22 | semidirect |
| 26. #819 | C22 | semidirect |
| 187. C2×C3 | #473 | semidirect |
| 201. C3 | C2×#473 | semidirect |
| 205. C2 | #5143 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#951 | 2 |
| C22×Dic12 | 2 |
| #5143 | 2 |
| C2×#824 | 2 |
| C2×#819 | 2 |
| C2×#473 | 3 |