Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
983 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 983 conjugacy classes of subgroups — too many to draw. Only its 105 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×A4×D9 | C2 | semidirect |
| 2. C2×C4×C9×A4 | C2 | semidirect |
| 3. A4×D36 | C2 | direct (N × H) |
| 5. C23×D36 | C3 | semidirect |
| 8. C2×A4×D9 | C22 | semidirect |
| 10. C4×C9×A4 | C22 | semidirect |
| 14. C24×D9 | C2×C3 | semidirect |
| 15. C23×C4×C9 | C2×C3 | semidirect |
| 20. C22×D36 | C2×C3 | semidirect |
| 23. C2×C9×A4 | D4 | semidirect |
| 41. C23×D9 | C22×C3 | semidirect |
| 46. C22×C4×C9 | C22×C3 | semidirect |
| 56. C2×D36 | A4 | direct (N × H) |
| 61. C9×A4 | C2×D4 | semidirect |
| 73. C2×C4×A4 | D9 | semidirect |
| 83. C23×C9 | C3×D4 | semidirect |
| 98. C22×D9 | C2×A4 | semidirect |
| 107. C2×C4×C9 | C2×A4 | semidirect |
| 111. D36 | C2×A4 | direct (N × H) |
| 143. C4×A4 | C2×D9 | semidirect |
| 157. C22×C9 | C2×C3×D4 | semidirect |
| 168. C2×D9 | C22×A4 | semidirect |
| 172. C4×C9 | C22×A4 | semidirect |
| 179. C23×C4 | C3×D9 | semidirect |
| 204. C2×A4 | D36 | direct (N × H) |
| 227. C2×C9 | D4×A4 | semidirect |
| 251. C22×C4 | C2×C3×D9 | semidirect |
| 276. A4 | C2×D36 | direct (N × H) |
| 283. C9 | C2×D4×A4 | semidirect |
| 301. C23 | C3×D36 | semidirect |
| 312. C2×C4 | A4×D9 | semidirect |
| 342. C22 | C2×C3×D36 | semidirect |
| 345. C4 | C2×A4×D9 | semidirect |
| 354. C2 | A4×D36 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A4×D9 | 2 |
| C2×C4×C9×A4 | 2 |
| A4×D36 | 2 |
| C2×A4×D12 | 3 |
| C23×D36 | 3 |
| C2×C3×D36 | 4 |