Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 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×C4×Q8 | C2 | semidirect |
| 3. C2×Q8×Dic3 | C2 | semidirect |
| 5. #4973 | C2 | semidirect |
| 7. #4929 | C2 | semidirect |
| 12. C2×D3×Q8 | C4 | semidirect |
| 28. C2×C4×Q8 | D3 | semidirect |
| 53. (C2×D3)⋊C4 | Q8 | direct (N × H) |
| 81. C3×Q8 | C22⋊C4 | semidirect |
| 90. C2×C3×C4 | C2×Q8 | semidirect |
| 99. C2×Dic3 | C2×Q8 | semidirect |
| 138. C2×D3 | C4×Q8 | semidirect |
| 154. Q8 | (C2×D3)⋊C4 | direct (N × H) |
| 172. C2×C4 | D3×Q8 | semidirect |
| 202. C3 | Q8×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×C3×C4×Q8 | 2 |
| C2×Q8×Dic3 | 2 |
| #4987 | 2 |
| #4973 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4929 | 2 |
| Q8×C22⋊C4 | 3 |