Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 4. C3×#63777 | C2 | semidirect |
| 5. C3×C4×#622 | C2 | semidirect |
| 6. #10593738 | C3 | direct (N × H) |
| 8. C3×#3792 | C4 | semidirect |
| 9. C2×C3×#622 | C4 | semidirect |
| 21. #63777 | C2×C3 | semidirect |
| 22. C4×#622 | C2×C3 | semidirect |
| 36. #3792 | C3×C4 | semidirect |
| 37. C2×#622 | C3×C4 | semidirect |
| 128. C33 | #405 | semidirect |
| 189. C32 | C3×#405 | semidirect |
| 219. C3 | #10593738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3792 | 2 |
| C22×C3×#622 | 2 |
| C3×#64086 | 2 |
| C3×#63777 | 2 |
| C3×C4×#622 | 2 |
| #10593738 | 3 |
| C3×#405 | 9 |