Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
367 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 91 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. D4×C9×A4 | C2 | semidirect |
| 2. C8×C9×A4 | C2 | semidirect |
| 4. C22×C9×D8 | C3 | semidirect |
| 5. D8×C22⋊C9 | C3 | semidirect |
| 11. C22×D4×C9 | C2×C3 | semidirect |
| 12. D4×C22⋊C9 | C2×C3 | semidirect |
| 16. C22×C8×C9 | C2×C3 | semidirect |
| 17. C8×C22⋊C9 | C2×C3 | semidirect |
| 23. A4×D8 | C9 | direct (N × H) |
| 38. C9×D8 | A4 | direct (N × H) |
| 42. C9×A4 | D8 | direct (N × H) |
| 45. D4×A4 | C2×C9 | semidirect |
| 50. C8×A4 | C2×C9 | semidirect |
| 66. D4×C9 | C2×A4 | semidirect |
| 71. C8×C9 | C2×A4 | semidirect |
| 72. C22×D8 | C3×C9 | semidirect |
| 101. C22×C9 | C3×D8 | semidirect |
| 102. C22⋊C9 | C3×D8 | semidirect |
| 106. C22×D4 | C2×C3×C9 | semidirect |
| 110. C22×C8 | C2×C3×C9 | semidirect |
| 146. D8 | C9×A4 | direct (N × H) |
| 159. A4 | C9×D8 | direct (N × H) |
| 165. C9 | A4×D8 | direct (N × H) |
| 174. D4 | C2×C9×A4 | semidirect |
| 178. C8 | C2×C9×A4 | semidirect |
| 194. C22 | C3×C9×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C9×A4 | 2 |
| C8×C9×A4 | 2 |
| C3×A4×D8 | 3 |
| C22×C9×D8 | 3 |
| D8×C22⋊C9 | 3 |
| C3×C9×D8 | 4 |