Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2632 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 2632 conjugacy classes of subgroups — too many to draw. Only its 463 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×C22⋊Q8 | C2 | semidirect |
| 3. C2×#88862 | C2 | semidirect |
| 4. #11722200 | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 8. C2×C33×Q8 | C22 | semidirect |
| 14. C33×C4⋊C4 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 19. C32×C22⋊Q8 | D3 | semidirect |
| 40. C2×C32×Q8 | C2×D3 | semidirect |
| 46. C32×C4⋊C4 | C2×D3 | semidirect |
| 52. C22×C33 | SD16 | semidirect |
| 63. C3×C22⋊Q8 | C3⋊D3 | semidirect |
| 89. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 95. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 101. C22×C32 | #215 | semidirect |
| 113. C22⋊Q8 | C3⋊(C3⋊D3) | semidirect |
| 116. C33 | #450 | semidirect |
| 138. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 146. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 150. C22×C3 | #3755 | semidirect |
| 160. C32 | #5046 | semidirect |
| 187. C22 | #88862 | semidirect |
| 193. C3 | #10592745 | semidirect |
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 |
| C33×C22⋊Q8 | 2 |
| C2×#88862 | 2 |
| #11722200 | 2 |
| #11722179 | 2 |
| #10592745 | 3 |