Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5229 | C2 | semidirect |
| 3. C2×#835 | C2 | semidirect |
| 6. C2×#817 | C2 | semidirect |
| 7. C2×C8×Dic3 | C2 | semidirect |
| 13. C2×C3×SD16 | C4 | semidirect |
| 68. C2×SD16 | Dic3 | semidirect |
| 109. C2×Dic3 | SD16 | semidirect |
| 110. C3×C8 | C22⋊C4 | semidirect |
| 193. C8 | #217 | semidirect |
| 218. C3 | #1968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SD16 | 2 |
| #5229 | 2 |
| C2×#835 | 2 |
| #5221 | 2 |
| C2×#832 | 2 |
| C2×#817 | 2 |
| C2×C8×Dic3 | 2 |
| #1968 | 3 |