Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
616 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 2. C2×C3⋊(C3⋊#157) | C2 | semidirect |
| 4. C22×C34 | C4 | semidirect |
| 6. C2×C32×C3⋊D3 | C4 | semidirect |
| 20. C22×C33 | Dic3 | semidirect |
| 22. C2×C3×C3⋊D3 | Dic3 | semidirect |
| 28. C34 | C22⋊C4 | semidirect |
| 52. C22×C32 | C3⋊Dic3 | semidirect |
| 53. C22×C32 | #157 | semidirect |
| 55. C2×C3⋊D3 | C3⋊Dic3 | semidirect |
| 64. C33 | #217 | semidirect |
| 92. C22×C3 | C3⋊#157 | semidirect |
| 101. C32 | #3757 | semidirect |
| 102. C32 | C22⋊#157 | semidirect |
| 118. C22 | C3⋊(C3⋊#157) | semidirect |
| 122. C3 | #88994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C3⋊D3 | 2 |
| C2×C3⋊(C3⋊#157) | 2 |
| #88994 | 3 |
| #3757 | 9 |