Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×D172 | C2 | semidirect |
| 2. #13063350 | C2 | direct (N × H) |
| 3. C2×#10621884 | C2 | semidirect |
| 4. C2×#10621882 | C2 | semidirect |
| 5. C2×#10621877 | C2 | semidirect |
| 6. C2×#41×C43 | C2 | semidirect |
| 9. #41×C43 | C22 | semidirect |
| 10. C2×Q8×C43 | C22 | semidirect |
| 12. C2×D4×C43 | C22 | semidirect |
| 18. C2×D172 | C22 | semidirect |
| 19. #10621884 | C22 | semidirect |
| 20. #10621882 | C22 | semidirect |
| 21. #10621877 | C22 | semidirect |
| 22. C2×C43⋊C8 | C22 | semidirect |
| 29. Q8×C43 | C23 | semidirect |
| 32. D4×C43 | C23 | semidirect |
| 42. C43⋊C8 | C23 | semidirect |
| 57. C2×C43 | AGL(1,ℤ/8) | semidirect |
| 61. C43 | C2×AGL(1,ℤ/8) | semidirect |
| 62. C2×#41 | D43 | semidirect |
| 70. #41 | C2×D43 | semidirect |
| 71. C2×Q8 | C2×D43 | semidirect |
| 77. C2×D4 | C2×D43 | semidirect |
| 90. Q8 | C22×D43 | semidirect |
| 96. D4 | C22×D43 | semidirect |
| 119. C2 | #13063350 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D172 | 2 |
| #13063350 | 2 |
| C2×#10621884 | 2 |
| C2×#10621882 | 2 |
| C2×#10621877 | 2 |
| C2×#41×C43 | 2 |
| C2×AGL(1,ℤ/8) | 43 |