Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
111 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 111 conjugacy classes of subgroups — too many to draw. Only its 50 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×C32×C8 | C2 | semidirect |
| 3. C2×C3×C3⋊C8 | C2 | semidirect |
| 5. (C2×D3)⋊C8 | C3 | direct (N × H) |
| 17. C2×C3×C8 | D3 | semidirect |
| 18. C2×C3×C8 | C2×C3 | semidirect |
| 19. C2×C3⋊C8 | C2×C3 | semidirect |
| 23. C2×C3×D3 | C8 | semidirect |
| 50. C2×C8 | C3×D3 | semidirect |
| 59. C2×D3 | C3×C8 | semidirect |
| 68. C32 | C22⋊C8 | semidirect |
| 95. C3 | (C2×D3)⋊C8 | direct (N × H) |
| 96. C3 | C3×C22⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D3 | 2 |
| C2×C32×C8 | 2 |
| C2×C3×C3⋊C8 | 2 |
| C3×C22⋊C8 | 3 |
| (C2×D3)⋊C8 | 3 |