Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
722 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 1. C2×C32×#204 | C2 | semidirect |
| 2. C3×#63863 | C2 | semidirect |
| 3. C2×C3×#3718 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 7. #10590867 | C3 | direct (N × H) |
| 23. C2×C3×#204 | D3 | semidirect |
| 24. C2×C3×#204 | C2×C3 | semidirect |
| 25. #63863 | C2×C3 | semidirect |
| 26. C2×#3718 | C2×C3 | semidirect |
| 28. C8×C3⋊Dic3 | C2×C3 | semidirect |
| 90. C2×#204 | C3×D3 | semidirect |
| 203. C33 | #495 | semidirect |
| 300. C32 | #5168 | semidirect |
| 301. C32 | C3×#495 | semidirect |
| 336. C3 | #10590867 | direct (N × H) |
| 337. C3 | C3×#5168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#204 | 2 |
| C3×#63863 | 2 |
| C2×C3×#3718 | 2 |
| C2×C3×#3713 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C3×#5168 | 3 |
| #10590867 | 3 |