Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13063353 | C2 | semidirect |
| 2. #14583449 | C2 | semidirect |
| 3. C2×#13063322 | C2 | semidirect |
| 4. #14583288 | C2 | semidirect |
| 5. #14583276 | C2 | semidirect |
| 6. #14583272 | C2 | semidirect |
| 7. C4×M16×C43 | C2 | semidirect |
| 12. C2×#10621873 | C22 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 14. #13063325 | C22 | semidirect |
| 18. #13063322 | C22 | semidirect |
| 19. #13063313 | C22 | semidirect |
| 24. #97×C43 | C22 | semidirect |
| 25. C4×C8×C43 | C22 | semidirect |
| 41. M16×C43 | D4 | semidirect |
| 71. C8×C43 | C2×D4 | semidirect |
| 82. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 97. C4×M16 | D43 | semidirect |
| 98. C43 | #3151 | semidirect |
| 115. #97 | C2×D43 | semidirect |
| 116. C4×C8 | C2×D43 | semidirect |
| 134. M16 | D172 | semidirect |
| 162. C8 | C2×D172 | semidirect |
| 174. C4 | #13063353 | semidirect |