Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 6. C34×C4 | C4 | semidirect |
| 7. C32×C3⋊Dic3 | C4 | semidirect |
| 21. C33×C4 | Dic3 | semidirect |
| 22. C3×C3⋊Dic3 | Dic3 | semidirect |
| 24. C34 | C4⋊C4 | semidirect |
| 47. C32×C4 | C3⋊Dic3 | semidirect |
| 48. C32×C4 | #157 | semidirect |
| 50. C3⋊Dic3 | C3⋊Dic3 | semidirect |
| 54. C33 | C4⋊Dic3 | semidirect |
| 76. C3×C4 | C3⋊#157 | semidirect |
| 83. C32 | C4⋊(C3⋊Dic3) | semidirect |
| 84. C32 | C4⋊#157 | semidirect |
| 97. C4 | C3⋊(C3⋊#157) | semidirect |
| 100. C3 | C4⋊(C3⋊#157) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊#157) | 2 |
| C32×C4×C3⋊D3 | 2 |
| C4⋊(C3⋊#157) | 3 |
| C4⋊(C3⋊Dic3) | 9 |