Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#10621902 | C2 | semidirect |
| 2. C2×D4×D43 | C2 | semidirect |
| 3. #13063352 | C2 | direct (N × H) |
| 4. C2×#10621884 | C2 | semidirect |
| 5. C2×D344 | C2 | semidirect |
| 6. C2×#10621882 | C2 | semidirect |
| 7. C2×#10621872 | C2 | semidirect |
| 8. C2×SD16×C43 | C2 | semidirect |
| 10. C2×Q8×C43 | C22 | semidirect |
| 14. #10621902 | C22 | semidirect |
| 16. D4×D43 | C22 | semidirect |
| 19. C2×D172 | C22 | semidirect |
| 22. SD16×C43 | C22 | semidirect |
| 23. C2×C8×C43 | C22 | semidirect |
| 24. #10621884 | C22 | semidirect |
| 25. #10621882 | C22 | semidirect |
| 26. C2×C43⋊C8 | C22 | semidirect |
| 27. D344 | C22 | semidirect |
| 28. #10621872 | C22 | semidirect |
| 36. Q8×C43 | C23 | semidirect |
| 47. D172 | C23 | semidirect |
| 51. C8×C43 | C23 | semidirect |
| 52. C43⋊C8 | C23 | semidirect |
| 68. C2×C43 | AGL(1,ℤ/8) | semidirect |
| 74. C43 | C2×AGL(1,ℤ/8) | semidirect |
| 79. C2×SD16 | D43 | semidirect |
| 86. C2×Q8 | C2×D43 | semidirect |
| 97. SD16 | C2×D43 | semidirect |
| 102. C2×C8 | C2×D43 | semidirect |
| 110. Q8 | C22×D43 | semidirect |
| 126. C8 | C22×D43 | semidirect |
| 145. C2 | #13063352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621902 | 2 |
| C2×D4×D43 | 2 |
| #13063352 | 2 |
| C2×#10621884 | 2 |
| C2×D344 | 2 |
| C2×#10621882 | 2 |
| C2×#10621872 | 2 |
| C2×SD16×C43 | 2 |
| C2×AGL(1,ℤ/8) | 43 |