Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 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. C2×C3×#102 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4987 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 17. C2×#237 | C4 | semidirect |
| 35. C2×#102 | D3 | semidirect |
| 124. C3×D4 | C22⋊C4 | semidirect |
| 152. Dic6 | C22⋊C4 | semidirect |
| 253. D4 | (C2×D3)⋊C4 | semidirect |
| 317. C3 | #1788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#237 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#816 | 2 |
| #4987 | 2 |
| C2×#810 | 2 |
| #1788 | 3 |