Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#13063257 | C2 | semidirect |
| 4. C2×#13063256 | C2 | semidirect |
| 5. #106×D43 | C2 | direct (N × H) |
| 6. C2×#106×C43 | C2 | semidirect |
| 10. C2×C8×D43 | C4 | semidirect |
| 16. #13063257 | C22 | semidirect |
| 17. #13063256 | C22 | semidirect |
| 20. #106×C43 | C22 | semidirect |
| 32. C2×C8×C43 | C2×C4 | semidirect |
| 39. C2×C43⋊C8 | C2×C4 | semidirect |
| 41. C8×D43 | C2×C4 | semidirect |
| 60. C8×C43 | C22×C4 | semidirect |
| 61. C43⋊C8 | C22×C4 | semidirect |
| 65. C2×D43 | #106 | direct (N × H) |
| 75. C2×C43 | C2×#106 | semidirect |
| 78. D43 | C2×#106 | direct (N × H) |
| 84. C2×#106 | D43 | direct (N × H) |
| 85. C43 | C22×#106 | semidirect |
| 99. #106 | C2×D43 | direct (N × H) |
| 114. C2×C8 | C4×D43 | semidirect |
| 140. C8 | C2×C4×D43 | semidirect |
| 154. C2 | #106×D43 | direct (N × H) |