Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11721335 | C2 | direct (N × H) |
| 2. C2×C9⋊(C42⋊C3) | C2 | semidirect |
| 4. C2×C9×#127 | C3 | semidirect |
| 5. C2×#127⋊C9 | C3 | semidirect |
| 7. C9⋊(C42⋊C3) | C22 | semidirect |
| 13. C9×#127 | C2×C3 | semidirect |
| 14. C2×C42×C9 | C2×C3 | semidirect |
| 15. #127⋊C9 | C2×C3 | semidirect |
| 16. C2×C42⋊C9 | C2×C3 | semidirect |
| 36. C42×C9 | C22×C3 | semidirect |
| 37. C42⋊C9 | C22×C3 | semidirect |
| 68. C2×#127 | 3−1+2 | semidirect |
| 106. #127 | C2×3−1+2 | semidirect |
| 107. C2×C42 | C2×3−1+2 | semidirect |
| 136. C2×C9 | #127⋊C3 | semidirect |
| 149. C42 | C22×3−1+2 | semidirect |
| 167. C9 | C2×#127⋊C3 | semidirect |
| 211. C2 | #11721335 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721335 | 2 |
| C2×C9⋊(C42⋊C3) | 2 |
| C2×C3×#127⋊C3 | 3 |
| C2×C9×#127 | 3 |
| C2×#127⋊C9 | 3 |
| C22×C9⋊A4 | 4 |