Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 461 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. C2×#88862 | C2 | semidirect |
| 4. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722179 | C2 | semidirect |
| 7. #11722178 | C2 | semidirect |
| 22. C32×C22⋊Q8 | D3 | semidirect |
| 44. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 61. C22×C33 | SD16 | semidirect |
| 72. C3×C22⋊Q8 | C3⋊D3 | semidirect |
| 116. C22×C32 | #215 | semidirect |
| 129. C22⋊Q8 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #465 | semidirect |
| 171. C22×C3 | #3755 | semidirect |
| 182. C32 | #5048 | semidirect |
| 209. C22 | #88862 | semidirect |
| 217. C3 | #10592747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊Q8 | 2 |
| C2×#88862 | 2 |
| #11723971 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722205 | 2 |
| #11722179 | 2 |
| #11722178 | 2 |
| #10592747 | 3 |