Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
211 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 4. C3×Dic3⋊C4 | C2 | direct (N × H) |
| 6. C2×Dic3⋊C4 | C3 | direct (N × H) |
| 11. C2×C3×Dic3 | C4 | semidirect |
| 22. Dic3⋊C4 | C2×C3 | direct (N × H) |
| 29. C3×Dic3 | C2×C4 | semidirect |
| 45. C2×Dic3 | C3×C4 | semidirect |
| 48. C2×C32 | C4⋊C4 | semidirect |
| 74. Dic3 | C2×C3×C4 | semidirect |
| 75. C32 | C2×C4⋊C4 | semidirect |
| 87. C2×C3 | Dic3⋊C4 | direct (N × H) |
| 88. C2×C3 | C3×C4⋊C4 | semidirect |
| 103. C3 | C2×Dic3⋊C4 | direct (N × H) |
| 104. C3 | C2×C3×C4⋊C4 | semidirect |
| 105. C2 | C3×Dic3⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4 | 2 |
| C22×C3×Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C2×C3×C4⋊C4 | 3 |
| C2×Dic3⋊C4 | 3 |