Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 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×#14273773 | C2 | semidirect |
| 2. C2×#14273755 | C2 | semidirect |
| 3. C2×#14273747 | C2 | semidirect |
| 4. #16837983 | C2 | semidirect |
| 5. #16837567 | C2 | semidirect |
| 6. #16837554 | C2 | semidirect |
| 7. #16837550 | C2 | semidirect |
| 8. #16837537 | C2 | semidirect |
| 9. C2×#14273647 | C2 | semidirect |
| 10. #16837370 | C2 | semidirect |
| 11. C59×#417 | C2 | semidirect |
| 17. C2×#11745685 | C22 | semidirect |
| 24. C2×#11745672 | C22 | semidirect |
| 25. C2×#11745660 | C22 | semidirect |
| 26. C2×#11745670 | C22 | semidirect |
| 27. C2×#11745671 | C22 | semidirect |
| 28. C2×D472 | C22 | semidirect |
| 29. C2×#11745669 | C22 | semidirect |
| 30. C22×C59⋊C8 | C22 | semidirect |
| 32. #14273707 | C22 | semidirect |
| 34. #14273702 | C22 | semidirect |
| 36. #14273647 | C22 | semidirect |
| 37. #14273647 | C22 | semidirect |
| 38. (C2×D59)⋊C8 | C22 | semidirect |
| 39. (C2×D59)⋊C8 | C22 | semidirect |
| 41. C2×M16×C59 | C22 | semidirect |
| 42. C2×C4⋊C4×C59 | C22 | semidirect |
| 43. #103×C59 | C22 | semidirect |
| 44. #102×C59 | C22 | semidirect |
| 48. #41×C59 | D4 | semidirect |
| 74. C2×D236 | D4 | semidirect |
| 187. #417 | D59 | semidirect |
| 190. C59 | #3012 | semidirect |
| 210. C2×M16 | C2×D59 | semidirect |
| 217. C2×C4⋊C4 | C2×D59 | semidirect |
| 218. #103 | C2×D59 | semidirect |
| 221. #102 | C2×D59 | semidirect |
| 234. #41 | D236 | semidirect |