Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #14582938 | C2 | direct (N × H) |
| 5. C2×#13063259 | C2 | semidirect |
| 6. C2×#13063258 | C2 | semidirect |
| 7. C2×#13063256 | C2 | semidirect |
| 8. C2×#106×C43 | C2 | semidirect |
| 11. C2×#10621872 | C4 | semidirect |
| 23. #13063259 | C22 | semidirect |
| 24. #13063258 | C22 | semidirect |
| 25. #13063256 | C22 | semidirect |
| 29. #106×C43 | C22 | semidirect |
| 43. C2×C8×C43 | C2×C4 | semidirect |
| 56. C2×C43⋊C8 | C2×C4 | semidirect |
| 58. #10621872 | C2×C4 | semidirect |
| 82. C8×C43 | C22×C4 | semidirect |
| 83. C43⋊C8 | C22×C4 | semidirect |
| 101. C2×C43 | #428 | semidirect |
| 113. C2×#106 | D43 | semidirect |
| 114. C43 | C2×#428 | semidirect |
| 135. #106 | C2×D43 | semidirect |
| 152. C2×C8 | C4×D43 | semidirect |
| 189. C8 | C2×C4×D43 | semidirect |
| 207. C2 | #14582938 | direct (N × H) |