Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
692 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 238 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 |
|---|---|---|
| 5. #10592382 | C3 | direct (N × H) |
| 103. C33 | #499 | semidirect |
| 144. C32 | #4683 | semidirect |
| 145. C32 | C3×#499 | semidirect |
| 163. C3 | C3×#4683 | semidirect |
| 164. C3 | #10592382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64079 | 2 |
| C33×C4×C8 | 2 |
| C3×#63645 | 2 |
| C3×#63644 | 2 |
| #10592382 | 3 |
| C3×#4683 | 3 |