Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3713 | C2 | semidirect |
| 2. C2×C3×#3708 | C2 | semidirect |
| 3. C3×#63734 | C2 | direct (N × H) |
| 4. C2×#63734 | C3 | direct (N × H) |
| 8. C3×#3713 | C22 | semidirect |
| 9. C3×#3708 | C22 | semidirect |
| 11. C2×#3713 | C2×C3 | semidirect |
| 12. C2×#3708 | C2×C3 | semidirect |
| 13. #63734 | C2×C3 | direct (N × H) |
| 30. #3713 | C22×C3 | semidirect |
| 31. #3708 | C22×C3 | semidirect |
| 61. C2×C33 | D16 | semidirect |
| 95. C33 | C2×D16 | semidirect |
| 120. C2×C32 | C3×D16 | semidirect |
| 149. C32 | C2×C3×D16 | semidirect |
| 163. C2×C3 | #63734 | direct (N × H) |
| 173. C3 | C2×#63734 | direct (N × H) |
| 175. C2 | C3×#63734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3713 | 2 |
| C2×C3×#3708 | 2 |
| C3×#63734 | 2 |
| C2×#63734 | 3 |
| C2×C3×D16 | 9 |