Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×D344 | C2 | semidirect |
| 2. D4×D172 | C2 | semidirect |
| 3. #14583276 | C2 | semidirect |
| 4. #14583135 | C2 | semidirect |
| 5. #14583095 | C2 | semidirect |
| 6. #14583035 | C2 | semidirect |
| 7. C4×D344 | C2 | semidirect |
| 8. C8×D4×C43 | C2 | semidirect |
| 9. C22×D172 | C22 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 14. C2×D344 | C22 | semidirect |
| 15. C2×D344 | C22 | semidirect |
| 16. #13063322 | C22 | semidirect |
| 18. #13063299 | C22 | semidirect |
| 20. C4×D172 | C22 | semidirect |
| 21. #13063259 | C22 | semidirect |
| 22. #13063247 | C22 | semidirect |
| 23. #13063247 | C22 | semidirect |
| 24. C22×C8×C43 | C22 | semidirect |
| 26. C4⋊C8×C43 | C22 | semidirect |
| 27. C22⋊C8×C43 | C22 | semidirect |
| 28. C4×C8×C43 | C22 | semidirect |
| 55. D344 | D4 | direct (N × H) |
| 62. D4×C43 | D8 | semidirect |
| 77. D172 | C2×D4 | semidirect |
| 81. C8×C43 | C2×D4 | semidirect |
| 84. C22×C43 | C2×D8 | semidirect |
| 95. C4×C43 | C2×D8 | semidirect |
| 113. C8×D4 | D43 | semidirect |
| 114. C43 | D4×D8 | semidirect |
| 122. C22×C8 | C2×D43 | semidirect |
| 130. C4⋊C8 | C2×D43 | semidirect |
| 133. C22⋊C8 | C2×D43 | semidirect |
| 134. C4×C8 | C2×D43 | semidirect |
| 176. D4 | D344 | direct (N × H) |
| 187. C8 | D4×D43 | semidirect |
| 197. C22 | C2×D344 | semidirect |
| 202. C4 | C2×D344 | semidirect |