Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063356 | C2 | semidirect |
| 3. #14583059 | C2 | semidirect |
| 4. #14583054 | C2 | semidirect |
| 5. #14583049 | C2 | semidirect |
| 6. #14582898 | C2 | semidirect |
| 7. #14582863 | C2 | semidirect |
| 8. C2×C22⋊Q8×C43 | C2 | semidirect |
| 19. C2×#10621885 | C22 | semidirect |
| 20. C2×#10621884 | C22 | semidirect |
| 21. C2×#10621877 | C22 | semidirect |
| 22. #13063248 | C22 | semidirect |
| 23. #13063245 | C22 | semidirect |
| 25. C22⋊(C43⋊C8) | C22 | semidirect |
| 26. C22×Q8×C43 | C22 | semidirect |
| 31. C22⋊Q8×C43 | C22 | semidirect |
| 33. C2×C4⋊C4×C43 | C22 | semidirect |
| 126. C22×C43 | #137 | semidirect |
| 149. C2×C22⋊Q8 | D43 | semidirect |
| 155. C43 | #3007 | semidirect |
| 162. C22×Q8 | C2×D43 | semidirect |
| 174. C22⋊Q8 | C2×D43 | semidirect |
| 176. C2×C4⋊C4 | C2×D43 | semidirect |
| 277. C22 | #13063356 | semidirect |