Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#890 | C2 | semidirect |
| 5. C2×#818 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4766 | C2 | direct (N × H) |
| 24. #890 | C22 | semidirect |
| 27. #818 | C22 | semidirect |
| 28. Dic3⋊C8 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 181. C2×C3 | #478 | semidirect |
| 201. C3 | C2×#478 | semidirect |
| 203. C2 | #4766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×#890 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#818 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#808 | 2 |
| #4766 | 2 |
| C2×#478 | 3 |