Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
329 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 329 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. Q8×C9×A4 | C2 | semidirect |
| 3. C8×C9×A4 | C2 | semidirect |
| 5. C22×C9×SD16 | C3 | semidirect |
| 6. SD16×C22⋊C9 | C3 | semidirect |
| 14. C22×Q8×C9 | C2×C3 | semidirect |
| 16. Q8×C22⋊C9 | C2×C3 | semidirect |
| 22. C22×C8×C9 | C2×C3 | semidirect |
| 23. C8×C22⋊C9 | C2×C3 | semidirect |
| 30. A4×SD16 | C9 | direct (N × H) |
| 52. C9×SD16 | A4 | direct (N × H) |
| 56. C9×A4 | SD16 | direct (N × H) |
| 61. Q8×A4 | C2×C9 | semidirect |
| 68. C8×A4 | C2×C9 | semidirect |
| 85. Q8×C9 | C2×A4 | semidirect |
| 97. C8×C9 | C2×A4 | semidirect |
| 98. C22×SD16 | C3×C9 | semidirect |
| 134. C22×C9 | C3×SD16 | semidirect |
| 135. C22⋊C9 | C3×SD16 | semidirect |
| 142. C22×Q8 | C2×C3×C9 | semidirect |
| 148. C22×C8 | C2×C3×C9 | semidirect |
| 196. SD16 | C9×A4 | direct (N × H) |
| 209. A4 | C9×SD16 | direct (N × H) |
| 218. C9 | A4×SD16 | direct (N × H) |
| 227. Q8 | C2×C9×A4 | semidirect |
| 237. C8 | C2×C9×A4 | semidirect |
| 253. C22 | C3×C9×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| D4×C9×A4 | 2 |
| C8×C9×A4 | 2 |
| C3×A4×SD16 | 3 |
| C22×C9×SD16 | 3 |
| SD16×C22⋊C9 | 3 |
| C3×C9×SD16 | 4 |