Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
805 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 805 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
| 2. D4×C9×A4 | C2 | semidirect |
| 3. C2×C4×C9×A4 | C2 | semidirect |
| 5. C22×C9×#41 | C3 | semidirect |
| 6. #41×C22⋊C9 | C3 | semidirect |
| 18. C22×Q8×C9 | C2×C3 | semidirect |
| 19. C22×D4×C9 | C2×C3 | semidirect |
| 20. C23×C4×C9 | C2×C3 | semidirect |
| 21. Q8×C22⋊C9 | C2×C3 | semidirect |
| 22. D4×C22⋊C9 | C2×C3 | semidirect |
| 23. C2×C4×C22⋊C9 | C2×C3 | semidirect |
| 30. A4×#41 | C9 | direct (N × H) |
| 44. C9×#41 | A4 | direct (N × H) |
| 59. C9×A4 | #41 | direct (N × H) |
| 69. Q8×A4 | C2×C9 | semidirect |
| 70. D4×A4 | C2×C9 | semidirect |
| 71. C2×C4×A4 | C2×C9 | semidirect |
| 87. Q8×C9 | C2×A4 | semidirect |
| 92. D4×C9 | C2×A4 | semidirect |
| 102. C2×C4×C9 | C2×A4 | semidirect |
| 103. C22×#41 | C3×C9 | semidirect |
| 141. C22×C9 | C3×#41 | semidirect |
| 143. C22⋊C9 | C3×#41 | semidirect |
| 154. C22×Q8 | C2×C3×C9 | semidirect |
| 155. C22×D4 | C2×C3×C9 | semidirect |
| 156. C23×C4 | C2×C3×C9 | semidirect |
| 200. #41 | C9×A4 | direct (N × H) |
| 222. A4 | C9×#41 | direct (N × H) |
| 231. C9 | A4×#41 | direct (N × H) |
| 239. Q8 | C2×C9×A4 | semidirect |
| 243. D4 | C2×C9×A4 | semidirect |
| 252. C2×C4 | C2×C9×A4 | semidirect |
| 267. C22 | C3×C9×#41 | 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 |
| C2×C4×C9×A4 | 2 |
| C3×A4×#41 | 3 |
| C22×C9×#41 | 3 |
| #41×C22⋊C9 | 3 |
| C3×C9×#41 | 4 |