Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
199 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 17. C9×SL(2,𝔽3) | Q8 | semidirect |
| 18. #5391 | C9 | direct (N × H) |
| 96. SL(2,𝔽3) | Q8×C9 | semidirect |
| 127. C9 | #5391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×SL(2,𝔽3) | 2 |
| C9×#859 | 2 |
| C3×#5391 | 3 |
| C9×#477 | 3 |
| C9×C4⋊Dic3 | 4 |