Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#13063242 | C2 | semidirect |
| 3. #14582685 | C2 | direct (N × H) |
| 4. C2×#99×C43 | C2 | semidirect |
| 5. C24×D43 | C4 | semidirect |
| 10. #13063293 | C4 | semidirect |
| 12. C2×C22⋊Dic43 | C4 | semidirect |
| 15. #13063242 | C22 | semidirect |
| 19. #99×C43 | C22 | semidirect |
| 27. C23×D43 | C2×C4 | semidirect |
| 43. C22⋊Dic43 | C2×C4 | semidirect |
| 122. C2×C43 | AΣL(1,𝔽16) | semidirect |
| 127. C2×#99 | D43 | semidirect |
| 129. C43 | C2×AΣL(1,𝔽16) | semidirect |
| 144. #99 | C2×D43 | semidirect |
| 247. C2 | #14582685 | direct (N × H) |