Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 138 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. C3×C9×#127 | C2 | semidirect |
| 2. C2×C3×#3673 | C2 | semidirect |
| 3. C3×#63436 | C2 | semidirect |
| 4. C3×C4×C9⋊C8 | C2 | semidirect |
| 6. #10588755 | C3 | direct (N × H) |
| 19. C9×#127 | C2×C3 | semidirect |
| 20. C2×#3673 | C2×C3 | semidirect |
| 21. #63436 | C2×C3 | semidirect |
| 22. C4×C9⋊C8 | C2×C3 | semidirect |
| 31. C3×C9⋊C8 | D4 | semidirect |
| 56. C3×C4×C9 | D8 | semidirect |
| 61. C3×#127 | D9 | semidirect |
| 89. C9⋊C8 | C3×D4 | semidirect |
| 129. C4×C9 | C3×D8 | semidirect |
| 133. #127 | C3×D9 | semidirect |
| 135. C3×C9 | #493 | semidirect |
| 192. C3×C4 | #3673 | semidirect |
| 198. C9 | C3×#493 | semidirect |
| 224. C4 | C3×#3673 | semidirect |
| 227. C3 | #10588755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C2×C3×#3673 | 2 |
| C3×#63436 | 2 |
| C3×C4×C9⋊C8 | 2 |
| C3×#5073 | 3 |
| #10588755 | 3 |