Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #4459 | C2 | direct (N × H) |
| 18. C3×C4×C8 | C22 | semidirect |
| 20. C4⋊(C3⋊C8) | C22 | semidirect |
| 23. C2×C4×C8 | D3 | semidirect |
| 32. C2×D12 | C8 | semidirect |
| 64. C4×C8 | C2×D3 | semidirect |
| 85. D12 | C2×C8 | semidirect |
| 159. C2×C3 | D4⋊C8 | semidirect |
| 181. C3 | C2×D4⋊C8 | semidirect |
| 183. C2 | #4459 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4459 | 2 |
| C2×D4⋊C8 | 3 |