Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1690 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
This group has 1690 conjugacy classes of subgroups — too many to draw. Only its 431 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×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C22×C3×C8×C9 | C2 | semidirect |
| 3. C2×#88525 | C2 | direct (N × H) |
| 9. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 10. C2×C3×C8×C9 | C22 | semidirect |
| 11. #88525 | C22 | direct (N × H) |
| 16. C22×C8×C9 | D3 | semidirect |
| 24. C4⋊(C3⋊D9) | C23 | semidirect |
| 25. C3×C8×C9 | C23 | semidirect |
| 38. C2×C8×C9 | C2×D3 | semidirect |
| 40. C22×C3×C9 | D8 | semidirect |
| 48. C22×C3×C8 | D9 | semidirect |
| 67. C8×C9 | C22×D3 | semidirect |
| 69. C2×C3×C9 | C2×D8 | semidirect |
| 80. C2×C3×C8 | C2×D9 | semidirect |
| 90. C22×C9 | D24 | semidirect |
| 98. C22×C8 | C3⋊D9 | semidirect |
| 99. C3×C9 | C22×D8 | semidirect |
| 114. C3×C8 | C22×D9 | semidirect |
| 119. C2×C9 | C2×D24 | semidirect |
| 127. C2×C8 | C2×C3⋊D9 | semidirect |
| 128. C22×C3 | D72 | semidirect |
| 141. C9 | C22×D24 | semidirect |
| 149. C8 | C22×C3⋊D9 | semidirect |
| 150. C2×C3 | C2×D72 | semidirect |
| 158. C22 | #88525 | direct (N × H) |
| 162. C3 | C22×D72 | semidirect |
| 165. C2 | C2×#88525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C22×C3×C8×C9 | 2 |
| C2×#88525 | 2 |
| C22×#3745 | 3 |
| C22×D72 | 3 |