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. C2×C33×M16 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722190 | C2 | semidirect |
| 18. C2×C32×M16 | D3 | semidirect |
| 57. C2×C3×M16 | C3⋊D3 | semidirect |
| 100. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 103. C33 | #408 | semidirect |
| 142. C32 | #5129 | semidirect |
| 170. C3 | #10592828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×M16 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722190 | 2 |
| #10592828 | 3 |