Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 635 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. C22×C33×C8 | C2 | semidirect |
| 3. #11723967 | C2 | semidirect |
| 4. #11722191 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 10. #89076 | C4 | semidirect |
| 20. C22×C32×C8 | D3 | semidirect |
| 63. C22×C3×C8 | C3⋊D3 | semidirect |
| 110. C22×C8 | C3⋊(C3⋊D3) | semidirect |
| 114. C33 | #416 | semidirect |
| 156. C32 | #5113 | semidirect |
| 186. C3 | #10592812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C22×C33×C8 | 2 |
| #11723967 | 2 |
| #11722191 | 2 |
| #11722186 | 2 |
| #10592812 | 3 |