Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
138 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 3. #10593255 | C3 | direct (N × H) |
| 6. C3×#3771 | C4 | semidirect |
| 18. #3771 | C3×C4 | semidirect |
| 54. C33 | #346 | semidirect |
| 83. C32 | C3×#346 | semidirect |
| 100. C3 | #10593255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64213 | 2 |
| C3×C8×#157 | 2 |
| #10593255 | 3 |
| C3×#346 | 9 |