Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 122 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⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 3. C32×#819 | C2 | semidirect |
| 19. C3×#819 | D3 | semidirect |
| 54. #819 | C3⋊D3 | semidirect |
| 113. C33 | #359 | semidirect |
| 162. C32 | #4497 | semidirect |
| 163. C32 | #4567 | semidirect |
| 186. C3 | #10589120 | semidirect |
| 187. C3 | #10589363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| C32×#819 | 2 |
| #10589363 | 3 |
| #10589120 | 3 |