Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×Dic36⋊C3 | C2 | semidirect |
| 4. #63377⋊C3 | C2 | semidirect |
| 5. #63376⋊C3 | C2 | semidirect |
| 7. #10588807 | C3 | semidirect |
| 25. C2×Dic36 | C2×C3 | semidirect |
| 26. #63377 | C2×C3 | semidirect |
| 27. #63376 | C2×C3 | semidirect |
| 159. 3−1+2 | #470 | semidirect |
| 218. C9 | C3×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×3−1+2 | 2 |
| #63486⋊C3 | 2 |
| C2×Dic36⋊C3 | 2 |
| #63377⋊C3 | 2 |
| #63376⋊C3 | 2 |
| C3×#5137 | 3 |
| #10588807 | 3 |