Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
329 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 117 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. C8×C9×A4 | C2 | semidirect |
| 4. C22×C9×M16 | C3 | semidirect |
| 5. M16×C22⋊C9 | C3 | semidirect |
| 17. C22×C8×C9 | C2×C3 | semidirect |
| 18. C8×C22⋊C9 | C2×C3 | semidirect |
| 24. A4×M16 | C9 | direct (N × H) |
| 43. C9×M16 | A4 | direct (N × H) |
| 47. C9×A4 | M16 | direct (N × H) |
| 56. C8×A4 | C2×C9 | semidirect |
| 80. C8×C9 | C2×A4 | semidirect |
| 81. C22×M16 | C3×C9 | semidirect |
| 113. C22×C9 | C3×M16 | semidirect |
| 115. C22⋊C9 | C3×M16 | semidirect |
| 126. C22×C8 | C2×C3×C9 | semidirect |
| 167. M16 | C9×A4 | direct (N × H) |
| 180. A4 | C9×M16 | direct (N × H) |
| 189. C9 | A4×M16 | direct (N × H) |
| 205. C8 | C2×C9×A4 | semidirect |
| 220. C22 | C3×C9×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9×A4 | 2 |
| C8×C9×A4 | 2 |
| C3×A4×M16 | 3 |
| C22×C9×M16 | 3 |
| M16×C22⋊C9 | 3 |
| C3×C9×M16 | 4 |