Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 133 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×(C2×D3)⋊C8 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 21. C2×C4×C8 | D3 | semidirect |
| 29. C2×D12 | C8 | semidirect |
| 36. C2×C3×C8 | D4 | semidirect |
| 94. C2×C8 | D12 | semidirect |
| 110. C3×C4 | C22⋊C8 | semidirect |
| 156. C4 | (C2×D3)⋊C8 | semidirect |
| 160. C3 | #1954 | semidirect |
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×(C2×D3)⋊C8 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #1954 | 3 |