Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
577 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 577 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10624891⋊C2 | C2 | direct (N × H) |
| 2. C2×#10624891 | C2 | semidirect |
| 3. C2×#92311 | C3 | semidirect |
| 4. C2×#92308 | C3 | semidirect |
| 5. C2×#6895⋊C2 | C3 | semidirect |
| 11. #10624891 | C22 | semidirect |
| 16. C2×#6898 | C2×C3 | semidirect |
| 21. C2×#6896 | C2×C3 | semidirect |
| 24. C2×#6895 | C2×C3 | semidirect |
| 32. C2×C9×3−1+2 | D3 | semidirect |
| 33. C2×C9×3−1+2 | D3 | semidirect |
| 35. C2×C3×C9⋊C9 | D3 | semidirect |
| 36. #92311 | C2×C3 | semidirect |
| 37. #92308 | C2×C3 | semidirect |
| 38. #6895⋊C2 | C2×C3 | semidirect |
| 66. #6898 | C22×C3 | semidirect |
| 71. #6896 | C22×C3 | semidirect |
| 74. #6895 | C22×C3 | semidirect |
| 82. C9×3−1+2 | C2×D3 | semidirect |
| 83. C9×3−1+2 | C2×D3 | semidirect |
| 85. C3×C9⋊C9 | C2×D3 | semidirect |
| 506. C2 | #10624891⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624891⋊C2 | 2 |
| C2×#10624891 | 2 |
| C2×#92311 | 3 |
| C2×#92308 | 3 |
| C2×#6895⋊C2 | 3 |
| C2×#92304 | 3 |
| C2×C9×AGL(1,ℤ/9) | 3 |
| C2×C9×(C3⋊D3)⋊C3 | 3 |
| C2×C3×D9⋊C9 | 3 |