Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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×Q8×D43 | C2 | semidirect |
| 3. C22×#10621873 | C2 | semidirect |
| 4. C22×#10621883 | C2 | semidirect |
| 5. C22×#10621884 | C2 | semidirect |
| 6. C2×SD16×D43 | C2 | direct (N × H) |
| 7. C22×C8×D43 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 11. C22×Dic86 | C22 | semidirect |
| 13. C2×Q8×D43 | C22 | semidirect |
| 20. C2×#10621873 | C22 | semidirect |
| 21. C2×#10621883 | C22 | semidirect |
| 22. C2×#10621884 | C22 | semidirect |
| 23. SD16×D43 | C22 | direct (N × H) |
| 24. C22×C43⋊C8 | C22 | semidirect |
| 25. C2×C8×D43 | C22 | semidirect |
| 26. C22×Q8×C43 | C22 | semidirect |
| 28. C2×SD16×C43 | C22 | semidirect |
| 29. C22×C8×C43 | C22 | semidirect |
| 36. C2×Q8×C43 | C23 | semidirect |
| 45. Q8×D43 | C23 | semidirect |
| 55. C2×Dic86 | C23 | semidirect |
| 56. SD16×C43 | C23 | semidirect |
| 57. C2×C8×C43 | C23 | semidirect |
| 58. #10621884 | C23 | semidirect |
| 59. #10621883 | C23 | semidirect |
| 60. C2×C43⋊C8 | C23 | semidirect |
| 61. #10621873 | C23 | semidirect |
| 62. C8×D43 | C23 | semidirect |
| 70. C22×D43 | SD16 | direct (N × H) |
| 73. Q8×C43 | C24 | semidirect |
| 89. Dic86 | C24 | semidirect |
| 90. C8×C43 | C24 | semidirect |
| 91. C43⋊C8 | C24 | semidirect |
| 94. C22×C43 | C2×SD16 | semidirect |
| 99. C2×D43 | C2×SD16 | direct (N × H) |
| 108. C2×C43 | C22×SD16 | semidirect |
| 111. D43 | C22×SD16 | direct (N × H) |
| 118. C22×SD16 | D43 | direct (N × H) |
| 120. C43 | C23×SD16 | semidirect |
| 126. C22×Q8 | C2×D43 | semidirect |
| 138. C2×SD16 | C2×D43 | direct (N × H) |
| 141. C22×C8 | C2×D43 | semidirect |
| 153. C2×Q8 | C22×D43 | semidirect |
| 171. SD16 | C22×D43 | direct (N × H) |
| 174. C2×C8 | C22×D43 | semidirect |
| 188. Q8 | C23×D43 | semidirect |
| 203. C8 | C23×D43 | semidirect |
| 211. C22 | SD16×D43 | direct (N × H) |
| 221. C2 | C2×SD16×D43 | direct (N × H) |