Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
648 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 82 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×C3×#3774 | C2 | semidirect |
| 2. C3×#63914 | C2 | semidirect |
| 3. C3×C4×#622 | C2 | semidirect |
| 4. #10593418 | C3 | direct (N × H) |
| 11. C2×#3774 | C2×C3 | semidirect |
| 13. #63914 | C2×C3 | semidirect |
| 14. C4×#622 | C2×C3 | semidirect |
| 22. C3×#622 | D4 | semidirect |
| 40. C33×C4 | D8 | semidirect |
| 41. C3×C3⋊Dic3 | D8 | semidirect |
| 66. #622 | C3×D4 | semidirect |
| 101. C32×C4 | C3×D8 | semidirect |
| 102. C3⋊Dic3 | C3×D8 | semidirect |
| 109. C33 | #493 | semidirect |
| 168. C3×C4 | #3774 | semidirect |
| 173. C32 | C3×#493 | semidirect |
| 201. C4 | C3×#3774 | semidirect |
| 204. C3 | #10593418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3774 | 2 |
| C3×#63914 | 2 |
| C3×C4×#622 | 2 |
| #10593418 | 3 |
| C3×#493 | 9 |