Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
972 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 292 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. C22×Q8×3−1+2 | C2 | semidirect |
| 3. C2×#3675⋊C3 | C2 | direct (N × H) |
| 4. C22×3−1+2⋊C8 | C2 | semidirect |
| 6. C22×#3675 | C3 | semidirect |
| 9. C2×Q8×3−1+2 | C22 | semidirect |
| 14. #3675⋊C3 | C22 | direct (N × H) |
| 15. C2×3−1+2⋊C8 | C22 | semidirect |
| 21. C22×Q8×C9 | C2×C3 | semidirect |
| 23. C2×#3675 | C2×C3 | semidirect |
| 24. C22×C9⋊C8 | C2×C3 | semidirect |
| 29. Q8×3−1+2 | C23 | semidirect |
| 35. 3−1+2⋊C8 | C23 | semidirect |
| 51. C2×Q8×C9 | C22×C3 | semidirect |
| 58. #3675 | C22×C3 | semidirect |
| 59. C2×C9⋊C8 | C22×C3 | semidirect |
| 60. C22×3−1+2 | SD16 | semidirect |
| 93. Q8×C9 | C23×C3 | semidirect |
| 102. C9⋊C8 | C23×C3 | semidirect |
| 104. C2×3−1+2 | C2×SD16 | semidirect |
| 134. C22×C9 | C3×SD16 | semidirect |
| 144. C22×Q8 | AGL(1,ℤ/9) | semidirect |
| 148. 3−1+2 | C22×SD16 | semidirect |
| 176. C2×C9 | C2×C3×SD16 | semidirect |
| 181. C2×Q8 | C2×AGL(1,ℤ/9) | semidirect |
| 204. C9 | C22×C3×SD16 | semidirect |
| 209. Q8 | C22×AGL(1,ℤ/9) | semidirect |
| 224. C22 | #3675⋊C3 | direct (N × H) |
| 232. C2 | C2×#3675⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×3−1+2 | 2 |
| C22×C4⋊AGL(1,ℤ/9) | 2 |
| C2×#3675⋊C3 | 2 |
| C22×3−1+2⋊C8 | 2 |
| C22×C3×#215 | 3 |
| C22×#3675 | 3 |