Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 181 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×C8 | C2 | semidirect |
| 4. C2×C4×C3⋊C8 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 17. (C2×D3)⋊C8 | C4 | direct (N × H) |
| 22. C2×C4×C8 | D3 | semidirect |
| 34. C2×C4×D3 | C8 | semidirect |
| 38. C2×C3×C8 | C2×C4 | semidirect |
| 46. C2×C3⋊C8 | C2×C4 | semidirect |
| 100. C2×C8 | C4×D3 | semidirect |
| 115. C2×D3 | C4×C8 | semidirect |
| 116. C3×C4 | C22⋊C8 | semidirect |
| 163. C4 | (C2×D3)⋊C8 | direct (N × H) |
| 166. C3 | C4×C22⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D3 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4550 | 2 |
| C4×C22⋊C8 | 3 |