Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 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 |
|---|---|---|
| 3. C2×#13063244 | C2 | semidirect |
| 4. C2×#13063243 | C2 | semidirect |
| 5. #101×D43 | C2 | direct (N × H) |
| 6. C2×#101×C43 | C2 | semidirect |
| 21. #13063244 | C22 | semidirect |
| 22. #13063243 | C22 | semidirect |
| 25. #101×C43 | C22 | semidirect |
| 102. C2×D43 | #101 | direct (N × H) |
| 113. C2×C43 | C2×#101 | semidirect |
| 116. D43 | C2×#101 | direct (N × H) |
| 122. C2×#101 | D43 | direct (N × H) |
| 123. C43 | C22×#101 | semidirect |
| 142. #101 | C2×D43 | direct (N × H) |
| 231. C2 | #101×D43 | direct (N × H) |