Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1602 conjugacy classes of subgroups; only the 426 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 426 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×C3×D36 | C2 | semidirect |
| 2. C2×C3×C42×C9 | C2 | semidirect |
| 3. C3×#63436 | C2 | direct (N × H) |
| 5. C2×#63436 | C3 | direct (N × H) |
| 9. C2×C3×D36 | C22 | semidirect |
| 10. C3×C42×C9 | C22 | semidirect |
| 14. C22×D36 | C2×C3 | semidirect |
| 16. C2×C42×C9 | C2×C3 | semidirect |
| 17. #63436 | C2×C3 | direct (N × H) |
| 21. C2×C3×C4×C9 | D4 | semidirect |
| 35. C2×D36 | C22×C3 | semidirect |
| 37. C42×C9 | C22×C3 | semidirect |
| 42. C3×C4×C9 | C2×D4 | semidirect |
| 47. C2×C3×C42 | D9 | semidirect |
| 62. C2×C4×C9 | C3×D4 | semidirect |
| 66. C2×C3×C9 | #127 | semidirect |
| 79. C3×C42 | C2×D9 | semidirect |
| 93. C4×C9 | C2×C3×D4 | semidirect |
| 96. C2×C42 | C3×D9 | semidirect |
| 97. C3×C9 | C2×#127 | semidirect |
| 108. C2×C3×C4 | D36 | semidirect |
| 118. C2×C9 | C3×#127 | semidirect |
| 125. C42 | C2×C3×D9 | semidirect |
| 137. C3×C4 | C2×D36 | semidirect |
| 141. C9 | C2×C3×#127 | semidirect |
| 146. C2×C4 | C3×D36 | semidirect |
| 151. C2×C3 | #63436 | direct (N × H) |
| 160. C4 | C2×C3×D36 | semidirect |
| 162. C3 | C2×#63436 | direct (N × H) |
| 165. C2 | C3×#63436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D36 | 2 |
| C2×C3×C42×C9 | 2 |
| C3×#63436 | 2 |
| C2×C3×#874 | 3 |
| C2×#63436 | 3 |