Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4620 conjugacy classes of subgroups; only the 1115 normal subgroups are shown.
This group has 4620 conjugacy classes of subgroups — too many to draw. Only its 1115 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. C22×#6308 | C2 | semidirect |
| 3. C2×C33×C42 | C2 | semidirect |
| 4. C2×#88859 | C2 | semidirect |
| 5. #11723916 | C2 | direct (N × H) |
| 14. C2×#6308 | C22 | semidirect |
| 15. C33×C42 | C22 | semidirect |
| 16. #88859 | C22 | semidirect |
| 19. C2×C32×C42 | D3 | semidirect |
| 43. C32×C42 | C2×D3 | semidirect |
| 56. C2×C3×C42 | C3⋊D3 | semidirect |
| 72. C2×C33 | #124 | semidirect |
| 84. C3×C42 | C2×C3⋊D3 | semidirect |
| 99. C2×C42 | C3⋊(C3⋊D3) | semidirect |
| 100. C33 | C2×#124 | semidirect |
| 113. C2×C32 | #875 | semidirect |
| 126. C42 | C2×C3⋊(C3⋊D3) | semidirect |
| 136. C32 | C2×#875 | semidirect |
| 149. C2×C3 | #64084 | semidirect |
| 162. C3 | C2×#64084 | semidirect |
| 164. C2 | #11723916 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×#6308 | 2 |
| C2×C33×C42 | 2 |
| C2×#88859 | 2 |
| #11723916 | 2 |
| C2×#64084 | 3 |