Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3388 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3388 conjugacy classes of subgroups — too many to draw. Only its 675 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. C33×C22⋊Q8 | C2 | semidirect |
| 2. #11723987 | C2 | semidirect |
| 4. #11723965 | C2 | semidirect |
| 5. #11723938 | C2 | semidirect |
| 6. #11723937 | C2 | semidirect |
| 7. #11723937 | C2 | semidirect |
| 9. #11723919 | C2 | semidirect |
| 12. C2×C33×Q8 | C22 | semidirect |
| 17. C2×#6308 | C22 | semidirect |
| 18. C2×#6308 | C22 | semidirect |
| 19. C33×C4⋊C4 | C22 | semidirect |
| 20. C33×C4⋊C4 | C22 | semidirect |
| 27. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 28. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 29. #88857 | C22 | semidirect |
| 30. #88857 | C22 | semidirect |
| 31. #88857 | C22 | semidirect |
| 32. C32×C22⋊Q8 | D3 | semidirect |
| 44. C22×C3⋊(C3⋊D3) | Q8 | semidirect |
| 62. C2×C32×Q8 | C2×D3 | semidirect |
| 69. C32×C4⋊C4 | C2×D3 | semidirect |
| 70. C32×C4⋊C4 | C2×D3 | semidirect |
| 97. C3×C22⋊Q8 | C3⋊D3 | semidirect |
| 132. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 139. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 140. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 173. C22⋊Q8 | C3⋊(C3⋊D3) | semidirect |
| 176. C33 | #543 | semidirect |
| 204. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 214. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 215. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 237. C32 | #5634 | semidirect |
| 277. C3 | #10596105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊Q8 | 2 |
| #11723987 | 2 |
| C2×#88859 | 2 |
| #11723965 | 2 |
| #11723938 | 2 |
| #11723937 | 2 |
| C22⋊C4×C3⋊(C3⋊D3) | 2 |
| #11723919 | 2 |
| #10596105 | 3 |