Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 94. C33 | #368 | semidirect |
| 145. C32 | #4493 | semidirect |
| 146. C32 | #4506 | semidirect |
| 167. C3 | #10589143 | semidirect |
| 168. C3 | #10589144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63646 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589144 | 3 |
| #10589143 | 3 |