Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
158 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 75. C33 | #333 | semidirect |
| 113. C32 | #4481 | semidirect |
| 137. C3 | #10593158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724365 | 2 |
| C3×C4⋊AGL(1,𝔽9) | 2 |
| #11722786 | 2 |
| #10593158 | 3 |
| #4481 | 9 |