Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4788 conjugacy classes of subgroups; only the 1115 normal subgroups are shown.
This group has 4788 conjugacy classes of subgroups — too many to draw. Only its 1115 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. C23×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×C33×C22⋊C4 | C2 | semidirect |
| 4. C2×#88859 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 6. #11723927 | C2 | direct (N × H) |
| 16. C22×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 17. C33×C22⋊C4 | C22 | semidirect |
| 18. #88859 | C22 | semidirect |
| 19. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 22. C2×C32×C22⋊C4 | D3 | semidirect |
| 51. C32×C22⋊C4 | C2×D3 | semidirect |
| 68. C2×C3×C22⋊C4 | C3⋊D3 | semidirect |
| 89. C2×C33 | #123 | semidirect |
| 102. C3×C22⋊C4 | C2×C3⋊D3 | semidirect |
| 122. C2×C22⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | C2×#123 | semidirect |
| 140. C2×C32 | #886 | semidirect |
| 155. C22⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 168. C32 | C2×#886 | semidirect |
| 185. C2×C3 | #64095 | semidirect |
| 201. C3 | C2×#64095 | semidirect |
| 204. C2 | #11723927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6312 | 2 |
| C23×C3⋊(C3⋊Dic3) | 2 |
| C2×C33×C22⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11723927 | 2 |
| C2×#64095 | 3 |