Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 875 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 875 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×#131 | C2 | semidirect |
| 3. #11723989 | C2 | semidirect |
| 4. #11723948 | C2 | semidirect |
| 5. M16×C3⋊(C3⋊D3) | C2 | semidirect |
| 6. #11723942 | C2 | semidirect |
| 7. C2×#88850 | C2 | semidirect |
| 16. C33×M16 | C22 | semidirect |
| 17. C2×C33×C8 | C22 | semidirect |
| 18. #88855 | C22 | semidirect |
| 19. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 22. #88850 | C22 | semidirect |
| 23. #88850 | C22 | semidirect |
| 24. C8×C3⋊(C3⋊D3) | C22 | semidirect |
| 26. C32×#131 | D3 | semidirect |
| 56. C32×M16 | C2×D3 | semidirect |
| 57. C2×C32×C8 | C2×D3 | semidirect |
| 74. C3×#131 | C3⋊D3 | semidirect |
| 108. C3×M16 | C2×C3⋊D3 | semidirect |
| 109. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 129. #131 | C3⋊(C3⋊D3) | semidirect |
| 132. C33 | #568 | semidirect |
| 165. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 168. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 177. C32 | #5750 | semidirect |
| 206. C3 | #10596221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊(C3⋊D3) | 2 |
| C33×#131 | 2 |
| #11723989 | 2 |
| #11723948 | 2 |
| M16×C3⋊(C3⋊D3) | 2 |
| #11723942 | 2 |
| C2×#88850 | 2 |
| #10596221 | 3 |