Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
589 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 589 conjugacy classes of subgroups — too many to draw. Only its 62 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. C9×C22⋊SL(2,𝔽3) | C2 | semidirect |
| 3. C22×C9×#41 | C3 | semidirect |
| 4. #10593123 | C3 | semidirect |
| 17. #5948 | C9 | direct (N × H) |
| 24. C9×#41 | A4 | semidirect |
| 40. C22⋊SL(2,𝔽3) | C2×C9 | semidirect |
| 58. C22×#41 | C3×C9 | semidirect |
| 80. C22×C9 | #41⋊C3 | semidirect |
| 117. #41 | C9×A4 | semidirect |
| 137. C9 | #5948 | direct (N × H) |
| 161. C22 | C9×#41⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊SL(2,𝔽3) | 2 |
| C3×#5948 | 3 |
| C22×C9×#41 | 3 |
| #10593123 | 3 |
| C9×#41⋊C3 | 4 |
| C4×C9×A4 | 4 |