Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4508 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.
This group has 4508 conjugacy classes of subgroups — too many to draw. Only its 1123 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×#6308 | C2 | semidirect |
| 3. C2×C33×C4⋊C4 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 6. #11723938 | C2 | direct (N × H) |
| 16. C2×#6308 | C22 | semidirect |
| 17. C33×C4⋊C4 | C22 | semidirect |
| 19. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 22. C2×C32×C4⋊C4 | D3 | semidirect |
| 29. C22×C3⋊(C3⋊D3) | Q8 | semidirect |
| 51. C32×C4⋊C4 | C2×D3 | semidirect |
| 61. C2×C3⋊(C3⋊D3) | C2×Q8 | semidirect |
| 68. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 88. C2×C33 | C22⋊Q8 | semidirect |
| 102. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 121. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | C2×C22⋊Q8 | semidirect |
| 139. C2×C32 | #897 | semidirect |
| 154. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 168. C32 | C2×#897 | semidirect |
| 184. C2×C3 | #64106 | semidirect |
| 201. C3 | C2×#64106 | semidirect |
| 203. C2 | #11723938 | direct (N × H) |
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 |
| C22×#6308 | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11723938 | 2 |
| C2×#64106 | 3 |