Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#816 | C2 | semidirect |
| 6. C2×C8×Dic3 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4768 | C2 | direct (N × H) |
| 24. #890 | C22 | semidirect |
| 27. #816 | C22 | semidirect |
| 28. C8×Dic3 | C22 | semidirect |
| 29. #810 | C22 | semidirect |
| 187. C2×C3 | #488 | semidirect |
| 207. C3 | C2×#488 | semidirect |
| 209. C2 | #4768 | 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 |
| C2×#890 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#816 | 2 |
| C2×C8×Dic3 | 2 |
| C2×#810 | 2 |
| #4768 | 2 |
| C2×#488 | 3 |