Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4620 conjugacy classes of subgroups; only the 1155 normal subgroups are shown.
This group has 4620 conjugacy classes of subgroups — too many to draw. Only its 1155 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 |
| 4. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 5. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 6. #11723933 | C2 | direct (N × H) |
| 13. C2×C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 15. C33×C4⋊C4 | C22 | semidirect |
| 17. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 18. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 20. C2×C32×C4⋊C4 | D3 | semidirect |
| 38. C4×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 47. C32×C4⋊C4 | C2×D3 | semidirect |
| 64. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 84. C2×C33 | #117 | semidirect |
| 96. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 115. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 118. C33 | C2×#117 | semidirect |
| 133. C2×C32 | #892 | semidirect |
| 146. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 161. C32 | C2×#892 | semidirect |
| 176. C2×C3 | #64101 | semidirect |
| 193. C3 | C2×#64101 | semidirect |
| 195. C2 | #11723933 | 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 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723933 | 2 |
| C2×#64101 | 3 |