Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
928 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 405 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 |
|---|---|---|
| 4. #5229 | C2 | direct (N × H) |
| 9. C22×C3×Q8 | C4 | semidirect |
| 29. C2×C3×Q8 | C2×C4 | semidirect |
| 42. C22×Dic3 | Q8 | semidirect |
| 49. C22×Q8 | Dic3 | semidirect |
| 81. C2×Dic3 | C2×Q8 | semidirect |
| 86. C2×Q8 | C2×Dic3 | semidirect |
| 140. C2×C3 | #391 | semidirect |
| 160. C3 | C2×#391 | semidirect |
| 161. C2 | #5229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×C4×Dic3 | 2 |
| #5229 | 2 |
| C2×C3⋊#95 | 2 |
| C2×#391 | 3 |