Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14583553 | C2 | semidirect |
| 2. D4×D172 | C2 | semidirect |
| 3. #14583246 | C2 | semidirect |
| 4. #14583213 | C2 | semidirect |
| 5. #14583180 | C2 | semidirect |
| 6. #14583135 | C2 | semidirect |
| 7. #14583095 | C2 | semidirect |
| 8. #14583035 | C2 | semidirect |
| 9. C4×D344 | C2 | semidirect |
| 10. C2×#13063247 | C2 | semidirect |
| 11. C8×D4×C43 | C2 | semidirect |
| 16. C2×D344 | C22 | semidirect |
| 17. #13063325 | C22 | semidirect |
| 23. #13063299 | C22 | semidirect |
| 26. C4×D172 | C22 | semidirect |
| 27. C2×C4⋊Dic43 | C22 | semidirect |
| 28. #13063259 | C22 | semidirect |
| 29. #13063259 | C22 | semidirect |
| 32. #13063247 | C22 | semidirect |
| 33. #13063247 | C22 | semidirect |
| 34. #13063247 | C22 | semidirect |
| 35. #13063247 | C22 | semidirect |
| 36. C22×C8×C43 | C22 | semidirect |
| 38. C4⋊C8×C43 | C22 | semidirect |
| 39. C22⋊C8×C43 | C22 | semidirect |
| 40. C4×C8×C43 | C22 | semidirect |
| 85. D4×C43 | D8 | semidirect |
| 106. D172 | #41 | semidirect |
| 152. C8×D4 | D43 | semidirect |
| 154. C43 | #3294 | semidirect |
| 160. C22×C8 | C2×D43 | semidirect |
| 175. C4⋊C8 | C2×D43 | semidirect |
| 182. C22⋊C8 | C2×D43 | semidirect |
| 183. C4×C8 | C2×D43 | semidirect |
| 240. D4 | D344 | semidirect |