Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
846 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 282 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×C3×C42×C9 | C2 | semidirect |
| 3. C2×C3×Dic9⋊C4 | C2 | semidirect |
| 4. C3×#63438 | C2 | direct (N × H) |
| 6. C2×#63438 | C3 | direct (N × H) |
| 10. C3×C42×C9 | C22 | semidirect |
| 12. C3×Dic9⋊C4 | C22 | semidirect |
| 18. C2×C42×C9 | C2×C3 | semidirect |
| 20. C2×Dic9⋊C4 | C2×C3 | semidirect |
| 21. #63438 | C2×C3 | direct (N × H) |
| 42. C42×C9 | C22×C3 | semidirect |
| 44. Dic9⋊C4 | C22×C3 | semidirect |
| 55. C2×C3×C42 | D9 | semidirect |
| 78. C2×C3×C9 | #126 | semidirect |
| 91. C3×C42 | C2×D9 | semidirect |
| 113. C2×C42 | C3×D9 | semidirect |
| 114. C3×C9 | C2×#126 | semidirect |
| 137. C2×C9 | C3×#126 | semidirect |
| 145. C42 | C2×C3×D9 | semidirect |
| 163. C9 | C2×C3×#126 | semidirect |
| 174. C2×C3 | #63438 | direct (N × H) |
| 186. C3 | C2×#63438 | direct (N × H) |
| 189. C2 | C3×#63438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C9 | 2 |
| C2×C3×(C2×D9)⋊C4 | 2 |
| C2×C3×Dic9⋊C4 | 2 |
| C3×#63438 | 2 |
| C2×C3×#876 | 3 |
| C2×#63438 | 3 |