Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 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 |
|---|---|---|
| 2. C22×Q8×D43 | C2 | semidirect |
| 3. C2×#13063354 | C2 | direct (N × H) |
| 4. C22×Dic172 | C2 | semidirect |
| 5. C22×#10621885 | C2 | semidirect |
| 6. C22×#10621883 | C2 | semidirect |
| 7. C22×#10621872 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 15. C2×Q8×D43 | C22 | semidirect |
| 20. #13063354 | C22 | direct (N × H) |
| 21. C2×Dic172 | C22 | semidirect |
| 22. C2×#10621885 | C22 | semidirect |
| 23. C2×#10621883 | C22 | semidirect |
| 24. C2×#10621872 | C22 | semidirect |
| 28. C2×SD16×C43 | C22 | semidirect |
| 44. Q8×D43 | C23 | semidirect |
| 55. SD16×C43 | C23 | semidirect |
| 57. #10621885 | C23 | semidirect |
| 58. #10621883 | C23 | semidirect |
| 60. Dic172 | C23 | semidirect |
| 61. #10621872 | C23 | semidirect |
| 91. C22×C43 | #137 | semidirect |
| 103. C2×C43 | C2×#137 | semidirect |
| 112. C22×SD16 | D43 | semidirect |
| 114. C43 | C22×#137 | semidirect |
| 132. C2×SD16 | C2×D43 | semidirect |
| 164. SD16 | C22×D43 | semidirect |
| 199. C22 | #13063354 | direct (N × H) |
| 209. C2 | C2×#13063354 | direct (N × H) |