Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C3×#63773 | C2 | semidirect |
| 3. C2×C3×#3708 | C2 | semidirect |
| 4. C3×#63765 | C2 | semidirect |
| 5. C3×#63764 | C2 | semidirect |
| 6. #10593772 | C3 | direct (N × H) |
| 17. #63773 | C2×C3 | semidirect |
| 18. C2×#3708 | C2×C3 | semidirect |
| 19. #63765 | C2×C3 | semidirect |
| 20. #63764 | C2×C3 | semidirect |
| 109. C33 | #504 | semidirect |
| 159. C32 | C3×#504 | semidirect |
| 183. C3 | #10593772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64116 | 2 |
| C3×#63773 | 2 |
| C2×C3×#3708 | 2 |
| C3×#63765 | 2 |
| C3×#63764 | 2 |
| #10593772 | 3 |
| C3×#504 | 9 |