Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063358 | C2 | semidirect |
| 3. C2×#13063355 | C2 | semidirect |
| 4. C2×#13063313 | C2 | semidirect |
| 5. #14583078 | C2 | direct (N × H) |
| 6. C2×#13063253 | C2 | semidirect |
| 7. C2×#13063241 | C2 | semidirect |
| 8. C2×#104×C43 | C2 | semidirect |
| 16. C22×Dic86 | C22 | semidirect |
| 22. #13063358 | C22 | semidirect |
| 24. #13063355 | C22 | semidirect |
| 29. C2×#10621877 | C22 | semidirect |
| 31. #13063313 | C22 | semidirect |
| 33. #13063253 | C22 | semidirect |
| 34. #13063241 | C22 | semidirect |
| 36. C2×M16×C43 | C22 | semidirect |
| 37. C2×C42×C43 | C22 | semidirect |
| 38. #104×C43 | C22 | semidirect |
| 84. C2×Dic86 | C23 | semidirect |
| 86. M16×C43 | C23 | semidirect |
| 89. C42×C43 | C23 | semidirect |
| 94. #10621877 | C23 | semidirect |
| 174. C2×C43 | #455 | semidirect |
| 184. C2×#104 | D43 | semidirect |
| 186. C43 | C2×#455 | semidirect |
| 209. C2×M16 | C2×D43 | semidirect |
| 213. C2×C42 | C2×D43 | semidirect |
| 215. #104 | C2×D43 | semidirect |
| 270. M16 | C22×D43 | semidirect |
| 275. C42 | C22×D43 | semidirect |
| 353. C2 | #14583078 | direct (N × H) |