Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×D172 | C2 | semidirect |
| 2. #14583227 | C2 | semidirect |
| 3. #14583210 | C2 | semidirect |
| 4. #14583196 | C2 | semidirect |
| 5. #14583111 | C2 | semidirect |
| 6. #14583049 | C2 | semidirect |
| 8. #14583009 | C2 | semidirect |
| 9. #14582997 | C2 | semidirect |
| 10. #14582956 | C2 | semidirect |
| 11. C43×#529 | C2 | semidirect |
| 22. #13063258 | C22 | semidirect |
| 23. #13063256 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 25. #13063249 | C22 | semidirect |
| 26. #13063246 | C22 | semidirect |
| 31. #13063236 | C22 | semidirect |
| 33. #125×C43 | C22 | semidirect |
| 34. #124×C43 | C22 | semidirect |
| 38. C4×Q8×C43 | C22 | semidirect |
| 40. C4×D4×C43 | C22 | semidirect |
| 141. #529 | D43 | semidirect |
| 152. C43 | #3114 | semidirect |
| 158. #125 | C2×D43 | semidirect |
| 159. #124 | C2×D43 | semidirect |
| 163. C4×Q8 | C2×D43 | semidirect |
| 169. C4×D4 | C2×D43 | semidirect |