Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2732 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 2732 conjugacy classes of subgroups — too many to draw. Only its 452 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×C32×Dic6 | C2 | semidirect |
| 3. C22×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C2×#88795 | C2 | direct (N × H) |
| 13. C2×C32×Dic6 | C22 | semidirect |
| 14. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. #88795 | C22 | direct (N × H) |
| 20. C22×C3×Dic6 | D3 | semidirect |
| 22. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 34. C32×Dic6 | C23 | semidirect |
| 35. C3×C3⋊(C3⋊C8) | C23 | semidirect |
| 55. C2×C3×Dic6 | C2×D3 | semidirect |
| 57. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 60. C22×C33 | SD16 | semidirect |
| 71. C22×Dic6 | C3⋊D3 | semidirect |
| 102. C3×Dic6 | C22×D3 | semidirect |
| 103. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 106. C2×C33 | C2×SD16 | semidirect |
| 126. C2×Dic6 | C2×C3⋊D3 | semidirect |
| 133. C22×C32 | #204 | semidirect |
| 134. C22×C32 | #215 | semidirect |
| 155. C33 | C22×SD16 | semidirect |
| 182. Dic6 | C22×C3⋊D3 | semidirect |
| 187. C2×C32 | C2×#204 | semidirect |
| 188. C2×C32 | C2×#215 | semidirect |
| 205. C22×C3 | #3717 | semidirect |
| 206. C22×C3 | #3755 | semidirect |
| 224. C32 | C22×#204 | semidirect |
| 225. C32 | C22×#215 | semidirect |
| 239. C2×C3 | C2×#3717 | semidirect |
| 240. C2×C3 | C2×#3755 | semidirect |
| 248. C22 | #88795 | direct (N × H) |
| 254. C3 | C22×#3717 | semidirect |
| 255. C3 | C22×#3755 | semidirect |
| 257. C2 | C2×#88795 | 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×C32×Dic6 | 2 |
| C22×C3×C3⋊(C3⋊C8) | 2 |
| C2×#88795 | 2 |
| C22×#3755 | 3 |
| C22×#3717 | 3 |