Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C3⋊#3771 | C2 | semidirect |
| 3. #11724237 | C2 | direct (N × H) |
| 10. C3⋊#3771 | C22 | semidirect |
| 31. C2×C3×C3⋊D3 | C16 | semidirect |
| 54. C2×C33 | C2×C16 | semidirect |
| 56. C3×C3⋊D3 | C2×C16 | semidirect |
| 67. C2×C3⋊D3 | C3⋊C16 | semidirect |
| 81. C33 | C22×C16 | semidirect |
| 100. C2×C32 | C2×C3⋊C16 | semidirect |
| 102. C3⋊D3 | C2×C3⋊C16 | semidirect |
| 126. C32 | C22×C3⋊C16 | semidirect |
| 140. C2×C3 | #64213 | semidirect |
| 151. C3 | C2×#64213 | semidirect |
| 153. C2 | #11724237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3787 | 2 |
| C2×C3⋊#3771 | 2 |
| #11724237 | 2 |
| C2×#64213 | 3 |
| C22×C3⋊C16 | 9 |