Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
161 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 66 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×Dic6 | C2 | semidirect |
| 3. C32×C4⋊C4 | C2 | semidirect |
| 6. C3×Dic3⋊C4 | C2 | semidirect |
| 7. C3×Dic3⋊C4 | C2 | semidirect |
| 9. #896 | C3 | direct (N × H) |
| 22. C2×Dic6 | C2×C3 | semidirect |
| 26. C3×C4⋊C4 | D3 | semidirect |
| 27. C3×C4⋊C4 | C2×C3 | semidirect |
| 32. Dic3⋊C4 | C2×C3 | semidirect |
| 33. Dic3⋊C4 | C2×C3 | semidirect |
| 37. C2×C3×D3 | Q8 | semidirect |
| 74. C4⋊C4 | C3×D3 | semidirect |
| 85. C2×D3 | C3×Q8 | semidirect |
| 101. C32 | C22⋊Q8 | semidirect |
| 133. C3 | #896 | direct (N × H) |
| 134. C3 | C3×C22⋊Q8 | 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×C3×Dic6 | 2 |
| C32×C4⋊C4 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C22⋊Q8 | 3 |
| #896 | 3 |