Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
430 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11720577 | C2 | semidirect |
| 6. C2×C3×D4×C9 | C4 | semidirect |
| 8. C3×C42×C9 | C4 | semidirect |
| 30. C2×D4×C9 | Dic3 | semidirect |
| 32. C42×C9 | Dic3 | semidirect |
| 69. C2×C3×D4 | Dic9 | semidirect |
| 73. C3×C42 | Dic9 | semidirect |
| 95. C3×C9 | #353 | semidirect |
| 121. C2×D4 | C3⋊Dic9 | semidirect |
| 124. C42 | C3⋊Dic9 | semidirect |
| 142. C9 | #4545 | semidirect |
| 167. C3 | #10588222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| #11720577 | 2 |
| #10589411 | 3 |
| #10588222 | 3 |