Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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×#803 | C2 | semidirect |
| 19. C2×C4⋊C8 | D3 | semidirect |
| 41. C2×C3⋊C8 | D4 | semidirect |
| 153. C3 | #1955 | 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×#803 | 2 |
| #1955 | 3 |