Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3752 conjugacy classes of subgroups; only the 835 normal subgroups are shown.
This group has 3752 conjugacy classes of subgroups — too many to draw. Only its 835 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. #11724684 | C2 | semidirect |
| 2. C33×#131 | C2 | semidirect |
| 3. #11723949 | C2 | semidirect |
| 4. #11723945 | C2 | semidirect |
| 5. C2×#88852 | C2 | semidirect |
| 10. #89076 | C22 | semidirect |
| 11. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 12. C33×M16 | C22 | semidirect |
| 13. C2×C33×C8 | C22 | semidirect |
| 14. #88853 | C22 | semidirect |
| 15. #88852 | C22 | semidirect |
| 16. #88852 | C22 | semidirect |
| 17. #88851 | C22 | semidirect |
| 19. C32×#131 | D3 | semidirect |
| 40. C32×M16 | C2×D3 | semidirect |
| 41. C2×C32×C8 | C2×D3 | semidirect |
| 53. C3×#131 | C3⋊D3 | semidirect |
| 77. C3×M16 | C2×C3⋊D3 | semidirect |
| 78. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 93. #131 | C3⋊(C3⋊D3) | semidirect |
| 94. C33 | #576 | semidirect |
| 118. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 119. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 126. C32 | #5752 | semidirect |
| 147. C3 | #10596223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724684 | 2 |
| C33×#131 | 2 |
| #11723949 | 2 |
| #11723945 | 2 |
| C2×#88852 | 2 |
| #10596223 | 3 |