Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 863 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 863 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×C4⋊C4 | C2 | semidirect |
| 3. C2×#88859 | C2 | semidirect |
| 4. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 12. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 17. C2×C32×C4⋊C4 | D3 | semidirect |
| 33. C2×C3⋊(C3⋊Dic3) | D4 | semidirect |
| 57. C33×C4 | C22⋊C4 | semidirect |
| 60. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 106. C32×C4 | (C2×D3)⋊C4 | semidirect |
| 109. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 112. C33 | #390 | semidirect |
| 155. C3×C4 | #3752 | semidirect |
| 157. C32 | #4988 | semidirect |
| 191. C4 | #88859 | semidirect |
| 192. C3 | #10592687 | semidirect |
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 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #10592687 | 3 |