Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1130 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 257 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×C3×Dic18 | C2 | semidirect |
| 3. C22×C9×C3⋊C8 | C2 | semidirect |
| 4. C2×#88416 | C2 | direct (N × H) |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 14. C2×C9×C3⋊C8 | C22 | semidirect |
| 15. #88416 | C22 | direct (N × H) |
| 22. C22×Dic18 | D3 | semidirect |
| 34. C3×Dic18 | C23 | semidirect |
| 35. C9×C3⋊C8 | C23 | semidirect |
| 57. C2×Dic18 | C2×D3 | semidirect |
| 60. C22×C3×C9 | SD16 | semidirect |
| 74. C22×C3⋊C8 | D9 | semidirect |
| 103. Dic18 | C22×D3 | semidirect |
| 106. C2×C3×C9 | C2×SD16 | semidirect |
| 129. C2×C3⋊C8 | C2×D9 | semidirect |
| 140. C22×C9 | #215 | semidirect |
| 155. C3×C9 | C22×SD16 | semidirect |
| 184. C3⋊C8 | C22×D9 | semidirect |
| 190. C2×C9 | C2×#215 | semidirect |
| 205. C22×C3 | #3664 | semidirect |
| 225. C9 | C22×#215 | semidirect |
| 239. C2×C3 | C2×#3664 | semidirect |
| 248. C22 | #88416 | direct (N × H) |
| 254. C3 | C22×#3664 | semidirect |
| 257. C2 | C2×#88416 | 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⋊D9) | 2 |
| C22×C3×Dic18 | 2 |
| C22×C9×C3⋊C8 | 2 |
| C2×#88416 | 2 |
| C22×#3717 | 3 |
| C22×#3664 | 3 |