Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 113 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. #5221 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×#817 | C2 | semidirect |
| 5. C2×#815 | C2 | semidirect |
| 10. C2×C3×D8 | C4 | semidirect |
| 49. C2×D8 | Dic3 | semidirect |
| 78. C3×C8 | C22⋊C4 | semidirect |
| 138. C8 | #217 | semidirect |
| 159. C3 | #1972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| #5221 | 2 |
| C2×#832 | 2 |
| C2×#817 | 2 |
| C2×#815 | 2 |
| #1972 | 3 |