Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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×#10621902 | C2 | semidirect |
| 2. C22×#10621900 | C2 | semidirect |
| 3. C2×#13063346 | C2 | direct (N × H) |
| 4. C22×#10621885 | C2 | semidirect |
| 5. C22×#10621873 | C2 | semidirect |
| 6. C22×#10621882 | C2 | semidirect |
| 7. C22×C8×D43 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 10. C2×#10621902 | C22 | semidirect |
| 12. C2×#10621900 | C22 | semidirect |
| 20. #13063346 | C22 | direct (N × H) |
| 21. C2×#10621885 | C22 | semidirect |
| 22. C2×#10621873 | C22 | semidirect |
| 23. C2×#10621882 | C22 | semidirect |
| 25. C2×C8×D43 | C22 | semidirect |
| 28. C2×SD16×C43 | C22 | semidirect |
| 44. #10621902 | C23 | semidirect |
| 46. #10621900 | C23 | semidirect |
| 55. SD16×C43 | C23 | semidirect |
| 57. #10621885 | C23 | semidirect |
| 58. #10621882 | C23 | semidirect |
| 60. #10621873 | C23 | semidirect |
| 61. C8×D43 | C23 | semidirect |
| 92. C22×C43 | #135 | semidirect |
| 105. C2×C43 | C2×#135 | semidirect |
| 114. C22×SD16 | D43 | semidirect |
| 117. C43 | C22×#135 | semidirect |
| 134. C2×SD16 | C2×D43 | semidirect |
| 166. SD16 | C22×D43 | semidirect |
| 205. C22 | #13063346 | direct (N × H) |
| 215. C2 | C2×#13063346 | direct (N × H) |