Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
720 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 260 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×C92 | C2 | semidirect |
| 2. C2×C3×C9×D9 | C2 | direct (N × H) |
| 5. C22×C9×D9 | C3 | direct (N × H) |
| 6. C2×C3×C92 | C22 | semidirect |
| 7. C3×C9×D9 | C22 | direct (N × H) |
| 14. C22×C92 | C2×C3 | semidirect |
| 15. C2×C9×D9 | C2×C3 | direct (N × H) |
| 16. C3×C92 | C23 | semidirect |
| 20. C22×C3×D9 | C9 | direct (N × H) |
| 28. C2×C92 | C22×C3 | semidirect |
| 29. C9×D9 | C22×C3 | direct (N × H) |
| 39. C22×C3×C9 | D9 | direct (N × H) |
| 40. C22×C3×C9 | C2×C9 | semidirect |
| 44. C2×C3×D9 | C2×C9 | direct (N × H) |
| 50. C92 | C23×C3 | semidirect |
| 55. C22×D9 | C3×C9 | direct (N × H) |
| 65. C2×C3×C9 | C2×D9 | direct (N × H) |
| 66. C2×C3×C9 | C22×C9 | semidirect |
| 70. C3×D9 | C22×C9 | direct (N × H) |
| 85. C22×C9 | C3×D9 | direct (N × H) |
| 86. C22×C9 | C2×C3×C9 | semidirect |
| 87. C2×D9 | C2×C3×C9 | direct (N × H) |
| 95. C3×C9 | C22×D9 | direct (N × H) |
| 96. C3×C9 | C23×C9 | semidirect |
| 115. C2×C9 | C2×C3×D9 | direct (N × H) |
| 116. C2×C9 | C22×C3×C9 | semidirect |
| 117. D9 | C22×C3×C9 | direct (N × H) |
| 122. C22×C3 | C9×D9 | direct (N × H) |
| 135. C9 | C22×C3×D9 | direct (N × H) |
| 136. C9 | C23×C3×C9 | semidirect |
| 142. C2×C3 | C2×C9×D9 | direct (N × H) |
| 147. C22 | C3×C9×D9 | direct (N × H) |
| 150. C3 | C22×C9×D9 | direct (N × H) |
| 154. C2 | C2×C3×C9×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C92 | 2 |
| C2×C3×C9×D9 | 2 |
| C22×C3×D3×C9 | 3 |
| C22×C32×D9 | 3 |
| C22×C9×D9 | 3 |