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×#13063355 | C2 | semidirect |
| 2. C2×#13063350 | C2 | semidirect |
| 3. C2×#13063313 | C2 | semidirect |
| 4. #14583291 | C2 | semidirect |
| 5. #14583286 | C2 | semidirect |
| 6. #14583281 | C2 | semidirect |
| 7. C4×#10621877 | C2 | semidirect |
| 8. C43×#532 | C2 | semidirect |
| 13. C2×#10621885 | C22 | semidirect |
| 14. C2×#10621883 | C22 | semidirect |
| 22. #13063236 | C22 | semidirect |
| 23. C4×C43⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C43 | C22 | semidirect |
| 26. #127×C43 | C22 | semidirect |
| 27. #124×C43 | C22 | semidirect |
| 59. #10621877 | D4 | semidirect |
| 109. #532 | D43 | semidirect |
| 115. C43 | #3153 | semidirect |
| 126. C4⋊Q8 | C2×D43 | semidirect |
| 127. #127 | C2×D43 | semidirect |
| 131. #124 | C2×D43 | semidirect |