Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
677 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 677 conjugacy classes of subgroups — too many to draw. Only its 87 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. A4×#611 | C2 | semidirect |
| 3. A4×D36 | C2 | semidirect |
| 4. C4×A4×D9 | C2 | semidirect |
| 5. A4×Dic18 | 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 | direct (N × H) |
| 86. C9×A4 | #41 | semidirect |
| 106. C2×C4×A4 | D9 | semidirect |
| 135. C2×C4×C9 | C2×A4 | semidirect |
| 140. #611 | C2×A4 | semidirect |
| 146. D36 | C2×A4 | semidirect |
| 151. C4×D9 | C2×A4 | semidirect |
| 155. Dic18 | C2×A4 | semidirect |
| 217. C22×C9 | C3×#41 | semidirect |
| 244. C23×C4 | C3×D9 | semidirect |
| 360. A4 | #3697 | direct (N × H) |
| 374. C9 | A4×#41 | semidirect |
| 412. C2×C4 | A4×D9 | semidirect |
| 438. C22 | C3×#3697 | 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 |
| A4×#611 | 2 |
| A4×D36 | 2 |
| C4×A4×D9 | 2 |
| A4×Dic18 | 2 |
| A4×#235 | 3 |
| C22×#3697 | 3 |
| C3×#3697 | 4 |