Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 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 |
|---|---|---|
| 1. C22×#10621883 | C2 | semidirect |
| 2. C2×#13063325 | C2 | semidirect |
| 3. #14583271 | C2 | direct (N × H) |
| 4. C2×C4×C43⋊C8 | C2 | semidirect |
| 8. C2×#10621883 | C22 | semidirect |
| 11. #13063325 | C22 | semidirect |
| 13. C4×C43⋊C8 | C22 | semidirect |
| 35. C2×C43⋊C8 | D4 | semidirect |
| 44. C2×C4×C43 | SD16 | semidirect |
| 53. C43⋊C8 | C2×D4 | semidirect |
| 61. C4×C43 | C2×SD16 | semidirect |
| 66. C2×C43 | #492 | semidirect |
| 74. C43 | C2×#492 | semidirect |
| 117. C2×C4 | #10621883 | semidirect |
| 131. C4 | C2×#10621883 | semidirect |
| 134. C2 | #14583271 | direct (N × H) |