Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×C4×Dic86 | C2 | semidirect |
| 4. C4×#10621873 | C2 | direct (N × H) |
| 5. C2×#13063257 | C2 | semidirect |
| 6. C2×#13063250 | C2 | semidirect |
| 8. C2×C4×C8×C43 | C2 | semidirect |
| 12. C2×#10621873 | C4 | direct (N × H) |
| 15. C4×Dic86 | C22 | semidirect |
| 23. #13063257 | C22 | semidirect |
| 24. #13063250 | C22 | semidirect |
| 29. C4×C8×C43 | C22 | semidirect |
| 45. C2×Dic86 | C2×C4 | semidirect |
| 48. C2×C8×C43 | C2×C4 | semidirect |
| 60. #10621873 | C2×C4 | direct (N × H) |
| 67. C2×C4×C43 | SD16 | semidirect |
| 86. Dic86 | C22×C4 | semidirect |
| 88. C8×C43 | C22×C4 | semidirect |
| 99. C4×C43 | C2×SD16 | semidirect |
| 106. C2×C43 | C4×SD16 | semidirect |
| 118. C2×C4×C8 | D43 | semidirect |
| 119. C43 | C2×C4×SD16 | semidirect |
| 140. C4×C8 | C2×D43 | semidirect |
| 160. C2×C8 | C4×D43 | semidirect |
| 191. C2×C4 | #10621873 | direct (N × H) |
| 199. C8 | C2×C4×D43 | semidirect |
| 213. C4 | C2×#10621873 | direct (N × H) |
| 217. C2 | C4×#10621873 | direct (N × H) |