Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
155 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 28 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 |
|---|---|---|
| 1. #10619580 | C2 | semidirect |
| 2. C32×#41⋊C3 | C3 | semidirect |
| 3. #41×H(3,𝔽3) | C3 | semidirect |
| 4. #88691 | C3 | semidirect |
| 6. C32×SL(2,𝔽3) | C2×C3 | semidirect |
| 10. #6204 | C2×C3 | semidirect |
| 51. H(3,𝔽3) | #41⋊C3 | semidirect |
| 69. #41 | AΣL(1,𝔽27) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619580 | 2 |
| C32×#41⋊C3 | 3 |
| #41×H(3,𝔽3) | 3 |
| #88691 | 3 |
| C4×AΣL(1,𝔽27) | 4 |