Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
197 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C32×C4⋊C4 | C2 | semidirect |
| 4. C3×C4⋊Dic3 | C2 | semidirect |
| 5. C3×Dic3⋊C4 | C2 | semidirect |
| 7. D3×C4⋊C4 | C3 | direct (N × H) |
| 14. C3×C4×D3 | C4 | semidirect |
| 22. C3×C4⋊C4 | D3 | direct (N × H) |
| 23. C3×C4⋊C4 | C2×C3 | semidirect |
| 24. C4⋊Dic3 | C2×C3 | semidirect |
| 25. Dic3⋊C4 | C2×C3 | semidirect |
| 31. C32×C4 | C2×C4 | semidirect |
| 33. C3×Dic3 | C2×C4 | semidirect |
| 50. C4×D3 | C3×C4 | semidirect |
| 54. C3×D3 | C4⋊C4 | direct (N × H) |
| 59. C4⋊C4 | C3×D3 | direct (N × H) |
| 75. C3×C4 | C4×D3 | semidirect |
| 76. C3×C4 | C2×C3×C4 | semidirect |
| 78. Dic3 | C2×C3×C4 | semidirect |
| 79. C32 | C2×C4⋊C4 | semidirect |
| 97. D3 | C3×C4⋊C4 | direct (N × H) |
| 105. C4 | C3×C4×D3 | semidirect |
| 107. C3 | D3×C4⋊C4 | direct (N × H) |
| 108. C3 | C2×C3×C4⋊C4 | 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 |
| C32×C4⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C2×C3×C4⋊C4 | 3 |
| D3×C4⋊C4 | 3 |