Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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. C33×#101 | C2 | semidirect |
| 3. C32×#836 | C2 | semidirect |
| 5. C3×#4477 | C3 | direct (N × H) |
| 17. C32×#101 | D3 | semidirect |
| 18. C32×#101 | C2×C3 | semidirect |
| 19. C3×#836 | C2×C3 | semidirect |
| 30. #4477 | C32 | direct (N × H) |
| 58. C3×#101 | C3×D3 | semidirect |
| 59. C3×#101 | C2×C32 | semidirect |
| 60. #836 | C2×C32 | semidirect |
| 124. #101 | C32×D3 | semidirect |
| 125. C33 | #355 | semidirect |
| 183. C32 | #4477 | direct (N × H) |
| 184. C32 | C3×#355 | semidirect |
| 210. C3 | C3×#4477 | direct (N × H) |
| 211. C3 | C32×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#947 | 2 |
| C33×#101 | 2 |
| C32×#836 | 2 |
| C32×#355 | 3 |
| C3×#4477 | 3 |