Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#13063350 | C2 | semidirect |
| 2. C2×M16×D43 | C2 | semidirect |
| 3. #14583406 | C2 | semidirect |
| 4. C2×#13063300 | C2 | semidirect |
| 5. #14583151 | C2 | semidirect |
| 6. #14583148 | C2 | semidirect |
| 7. #14583134 | C2 | semidirect |
| 8. #14583131 | C2 | semidirect |
| 9. #14582939 | C2 | semidirect |
| 10. #14582905 | C2 | semidirect |
| 11. C43×#417 | C2 | semidirect |
| 16. C2×#10621884 | C22 | semidirect |
| 17. C2×#10621882 | C22 | semidirect |
| 19. C2×#10621872 | C22 | semidirect |
| 21. C2×C8×D43 | C22 | semidirect |
| 23. #13063301 | C22 | semidirect |
| 24. #13063301 | C22 | semidirect |
| 29. #13063296 | C22 | semidirect |
| 30. #13063296 | C22 | semidirect |
| 36. #13063258 | C22 | semidirect |
| 37. #13063256 | C22 | semidirect |
| 38. #13063247 | C22 | semidirect |
| 39. #13063247 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 44. #102×C43 | C22 | semidirect |
| 89. #10621877 | D4 | semidirect |
| 136. C43⋊C8 | C2×D4 | semidirect |
| 154. C2×D43 | AGL(1,ℤ/8) | semidirect |
| 183. #417 | D43 | semidirect |
| 184. C43 | #3055 | semidirect |
| 214. #103 | C2×D43 | semidirect |
| 217. #102 | C2×D43 | semidirect |