Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 551 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 551 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 |
|---|---|---|
| 7. C3×C42×C9 | C4 | semidirect |
| 26. C42×C9 | Dic3 | semidirect |
| 31. C3×C4×C9 | C4⋊C4 | semidirect |
| 55. C3×C42 | Dic9 | semidirect |
| 67. C4×C9 | C4⋊Dic3 | semidirect |
| 71. C3×C9 | #384 | semidirect |
| 91. C42 | C3⋊Dic9 | semidirect |
| 98. C3×C4 | C4⋊Dic9 | semidirect |
| 103. C9 | #4935 | semidirect |
| 119. C4 | C4⋊(C3⋊Dic9) | semidirect |
| 120. C3 | #10588615 | semidirect |
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×C4⋊(C3⋊Dic9) | 2 |
| #10592634 | 3 |
| #10588615 | 3 |