Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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. C2×#887 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4767 | C2 | direct (N × H) |
| 26. C2×Dic12 | C22 | semidirect |
| 28. #887 | C22 | semidirect |
| 30. Dic3⋊C8 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 205. C2×C3 | #464 | semidirect |
| 225. C3 | C2×#464 | semidirect |
| 227. C2 | #4767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C22×#214 | 2 |
| C22×Dic12 | 2 |
| C2×#887 | 2 |
| C2×C3×#102 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#810 | 2 |
| #4767 | 2 |
| C2×#464 | 3 |