Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
274 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 62 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×#64243 | C2 | semidirect |
| 5. C3×#63746 | C2 | semidirect |
| 6. C3×#63745 | C2 | semidirect |
| 7. C3×#63744 | C2 | semidirect |
| 8. #10593557 | C3 | direct (N × H) |
| 21. #64243 | C2×C3 | semidirect |
| 24. #63746 | C2×C3 | semidirect |
| 25. #63745 | C2×C3 | semidirect |
| 26. #63744 | C2×C3 | semidirect |
| 137. C33 | #478 | semidirect |
| 203. C32 | C3×#478 | semidirect |
| 243. C3 | #10593557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×#157 | 2 |
| C3×#64243 | 2 |
| C3×#63782 | 2 |
| C3×#63746 | 2 |
| C3×#63745 | 2 |
| C3×#63744 | 2 |
| #10593557 | 3 |
| C3×#478 | 9 |