Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
846 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 333 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×C9×Dic3⋊C4 | C2 | semidirect |
| 4. C9×#876 | C2 | direct (N × H) |
| 10. C3×C42×C9 | C22 | semidirect |
| 12. C9×Dic3⋊C4 | C22 | semidirect |
| 21. C2×C42×C9 | D3 | semidirect |
| 30. C2×#876 | C9 | direct (N × H) |
| 44. C42×C9 | C2×D3 | semidirect |
| 55. C2×C3×C42 | C2×C9 | semidirect |
| 58. C2×Dic3⋊C4 | C2×C9 | semidirect |
| 59. #876 | C2×C9 | direct (N × H) |
| 78. C2×C3×C9 | #126 | semidirect |
| 91. C3×C42 | C22×C9 | semidirect |
| 94. Dic3⋊C4 | C22×C9 | semidirect |
| 113. C2×C42 | D3×C9 | semidirect |
| 114. C3×C9 | C2×#126 | semidirect |
| 138. C2×C9 | #876 | direct (N × H) |
| 145. C42 | C2×D3×C9 | semidirect |
| 163. C9 | C2×#876 | direct (N × H) |
| 174. C2×C3 | C9×#126 | semidirect |
| 186. C3 | C2×C9×#126 | semidirect |
| 189. C2 | C9×#876 | 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×C9×(C2×D3)⋊C4 | 2 |
| C2×C9×Dic3⋊C4 | 2 |
| C9×#876 | 2 |
| C2×C3×#876 | 3 |
| C2×C9×#126 | 3 |