Finite Group DatabasebetaFinite Group Databasebeta← C3×(C3×SL(2,𝔽3))⋊C9 #14517234
Order 1944.
482 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 136 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. C32×Q8×C9 | C3 | semidirect |
| 3. C32×Q8⋊C9 | C3 | semidirect |
| 4. (C3×SL(2,𝔽3))⋊C9 | C3 | direct (N × H) |
| 11. C32×SL(2,𝔽3) | C9 | semidirect |
| 14. C3×Q8×C9 | C32 | semidirect |
| 16. C3×Q8⋊C9 | C32 | semidirect |
| 26. C32×C9 | SL(2,𝔽3) | semidirect |
| 35. C3×SL(2,𝔽3) | C3×C9 | semidirect |
| 60. C3×C9 | C3×SL(2,𝔽3) | semidirect |
| 61. C3×Q8 | C32⋊C9 | semidirect |
| 90. Q8 | C3×C32⋊C9 | semidirect |
| 98. C3 | (C3×SL(2,𝔽3))⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×SL(2,𝔽3) | 3 |
| C32×Q8×C9 | 3 |
| C32×Q8⋊C9 | 3 |
| (C3×SL(2,𝔽3))⋊C9 | 3 |
| C2×C3×C32⋊C9 | 4 |