Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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. C2×#13063358 | C2 | semidirect |
| 2. C2×#13063355 | C2 | semidirect |
| 3. C2×#13063351 | C2 | semidirect |
| 4. #14583445 | C2 | semidirect |
| 5. C2×#13063312 | C2 | semidirect |
| 6. #14583290 | C2 | semidirect |
| 7. #14583287 | C2 | semidirect |
| 8. #14583282 | C2 | semidirect |
| 9. #14583280 | C2 | semidirect |
| 10. M16×Dic43 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C43 | C2 | semidirect |
| 17. C2×Dic172 | C22 | semidirect |
| 18. C2×#10621885 | C22 | semidirect |
| 19. C2×#10621873 | C22 | semidirect |
| 21. C2×#10621883 | C22 | semidirect |
| 24. #13063323 | C22 | semidirect |
| 25. #13063321 | C22 | semidirect |
| 26. #13063314 | C22 | semidirect |
| 30. #13063312 | C22 | semidirect |
| 35. #13063235 | C22 | semidirect |
| 36. C8×Dic43 | C22 | semidirect |
| 70. M16×C43 | D4 | semidirect |
| 84. #10621877 | D4 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D43 | semidirect |
| 162. C43 | #3153 | semidirect |
| 228. M16 | C22⋊D43 | semidirect |