Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13063290 | C2 | semidirect |
| 4. #14582998 | C2 | direct (N × H) |
| 5. C2×#13063248 | C2 | semidirect |
| 7. C2×#13063235 | C2 | semidirect |
| 8. C2×#107×C43 | C2 | semidirect |
| 12. C2×#10621873 | C4 | semidirect |
| 16. #13063290 | C22 | semidirect |
| 23. #13063248 | C22 | semidirect |
| 25. #13063235 | C22 | semidirect |
| 29. #107×C43 | C22 | semidirect |
| 45. C2×Dic86 | C2×C4 | semidirect |
| 47. C2×C8×C43 | C2×C4 | semidirect |
| 60. #10621873 | C2×C4 | semidirect |
| 86. Dic86 | C22×C4 | semidirect |
| 87. C8×C43 | C22×C4 | semidirect |
| 106. C2×C43 | #440 | semidirect |
| 115. C2×#107 | D43 | semidirect |
| 119. C43 | C2×#440 | semidirect |
| 137. #107 | C2×D43 | semidirect |
| 161. C2×C8 | C4×D43 | semidirect |
| 199. C8 | C2×C4×D43 | semidirect |
| 217. C2 | #14582998 | direct (N × H) |