Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
892 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 892 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 1. C2×C33×D8 | C2 | semidirect |
| 2. C2×C3×#3745 | C2 | semidirect |
| 3. C3×#63653 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 5. C2×#63653 | C3 | direct (N × H) |
| 10. C33×D8 | C22 | semidirect |
| 13. C3×#3745 | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 16. C2×C32×D8 | D3 | semidirect |
| 17. C2×C32×D8 | C2×C3 | semidirect |
| 18. C2×#3745 | C2×C3 | semidirect |
| 20. #63653 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 44. C32×D8 | C2×D3 | semidirect |
| 45. C32×D8 | C22×C3 | semidirect |
| 50. #3745 | C22×C3 | semidirect |
| 53. C3⋊(C3⋊C16) | C22×C3 | semidirect |
| 64. C2×C3×D8 | C3×D3 | semidirect |
| 65. C2×C3×D8 | C3⋊D3 | semidirect |
| 97. C2×C33 | D16 | semidirect |
| 111. C3×D8 | C2×C3×D3 | semidirect |
| 112. C3×D8 | C2×C3⋊D3 | semidirect |
| 140. C2×D8 | C3×C3⋊D3 | semidirect |
| 143. C33 | C2×D16 | semidirect |
| 173. C2×C32 | #826 | semidirect |
| 174. C2×C32 | C3×D16 | semidirect |
| 184. D8 | C2×C3×C3⋊D3 | semidirect |
| 207. C32 | C2×#826 | semidirect |
| 208. C32 | C2×C3×D16 | semidirect |
| 224. C2×C3 | C3×#826 | semidirect |
| 225. C2×C3 | #63653 | direct (N × H) |
| 237. C3 | C2×C3×#826 | semidirect |
| 238. C3 | C2×#63653 | direct (N × H) |
| 241. C2 | C3×#63653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C2×C3×#3745 | 2 |
| C3×#63653 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| C2×#63653 | 3 |
| C2×C3×#826 | 3 |