Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×Q8⋊C8 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 34. Q8⋊C8 | D3 | direct (N × H) |
| 37. D3×Q8 | C8 | semidirect |
| 87. C3×Q8 | C2×C8 | semidirect |
| 107. Dic6 | C2×C8 | semidirect |
| 164. Q8 | D3×C8 | semidirect |
| 189. D3 | Q8⋊C8 | direct (N × H) |
| 206. C3 | C2×Q8⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Q8 | 2 |
| D3×C4⋊C8 | 2 |
| C4×D3×C8 | 2 |
| C3×Q8⋊C8 | 2 |
| #4535 | 2 |
| #4484 | 2 |
| #4456 | 2 |
| C2×Q8⋊C8 | 3 |