Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×D172 | C2 | semidirect |
| 2. #14583247 | C2 | semidirect |
| 3. #14583212 | C2 | semidirect |
| 4. #14583176 | C2 | semidirect |
| 5. #14583133 | C2 | semidirect |
| 6. #14583094 | C2 | semidirect |
| 7. #14583032 | C2 | semidirect |
| 8. C4×#10621882 | C2 | semidirect |
| 9. D4×C43⋊C8 | C2 | semidirect |
| 10. C2×#13063245 | C2 | semidirect |
| 11. C43×#547 | C2 | semidirect |
| 15. C2×#10621882 | C22 | semidirect |
| 16. C22×C43⋊C8 | C22 | semidirect |
| 22. #13063258 | C22 | semidirect |
| 23. #13063258 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 25. #13063246 | C22 | semidirect |
| 28. #13063245 | C22 | semidirect |
| 29. #13063245 | C22 | semidirect |
| 30. #13063245 | C22 | semidirect |
| 31. C22⋊(C43⋊C8) | C22 | semidirect |
| 32. C4×C43⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C43 | C22 | semidirect |
| 37. #121×C43 | C22 | semidirect |
| 39. C4×D4×C43 | C22 | semidirect |
| 40. C2×C4⋊C4×C43 | C22 | semidirect |
| 89. D4×C43 | D8 | semidirect |
| 108. D172 | #41 | semidirect |
| 143. #547 | D43 | semidirect |
| 154. C43 | #3294 | semidirect |
| 161. C4⋊Q8 | C2×D43 | semidirect |
| 167. #121 | C2×D43 | semidirect |
| 171. C4×D4 | C2×D43 | semidirect |
| 172. C2×C4⋊C4 | C2×D43 | semidirect |
| 240. D4 | #10621882 | semidirect |