Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
661 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 661 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×C4×C9⋊A4 | C2 | semidirect |
| 2. #611⋊A4 | C2 | semidirect |
| 3. C4⋊(D9⋊A4) | C2 | semidirect |
| 4. C4×D9⋊A4 | C2 | semidirect |
| 5. Dic18⋊A4 | C2 | semidirect |
| 7. C22×#3697 | C3 | semidirect |
| 19. C23×C4×C9 | C2×C3 | semidirect |
| 20. C22×#611 | C2×C3 | semidirect |
| 27. C22×D36 | C2×C3 | semidirect |
| 28. C22×C4×D9 | C2×C3 | semidirect |
| 29. C22×Dic18 | C2×C3 | semidirect |
| 71. #3697 | A4 | semidirect |
| 86. C9⋊A4 | #41 | semidirect |
| 134. C2×C4×C9 | C2×A4 | semidirect |
| 139. #611 | C2×A4 | semidirect |
| 145. D36 | C2×A4 | semidirect |
| 150. C4×D9 | C2×A4 | semidirect |
| 154. Dic18 | C2×A4 | semidirect |
| 213. C22×C9 | C3×#41 | semidirect |
| 240. C23×C4 | AGL(1,ℤ/9) | semidirect |
| 363. C9 | A4×#41 | semidirect |
| 401. C2×C4 | D9⋊A4 | semidirect |
| 425. C22 | #3697⋊C3 | 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 |
| #611⋊A4 | 2 |
| C4⋊(D9⋊A4) | 2 |
| C4×D9⋊A4 | 2 |
| Dic18⋊A4 | 2 |
| A4×#235 | 3 |
| C22×#3697 | 3 |
| #3697⋊C3 | 4 |