Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273751 | C2 | semidirect |
| 2. #16838056 | C2 | semidirect |
| 3. D4×D236 | C2 | semidirect |
| 4. #16837775 | C2 | semidirect |
| 5. #16837649 | C2 | semidirect |
| 6. #16837607 | C2 | semidirect |
| 7. #16837597 | C2 | semidirect |
| 8. #16837554 | C2 | semidirect |
| 9. #16837548 | C2 | semidirect |
| 10. #16837481 | C2 | semidirect |
| 11. C4×D8×C59 | C2 | semidirect |
| 12. C2×#11745687 | C22 | semidirect |
| 16. C2×#11745660 | C22 | semidirect |
| 17. C2×#11745660 | C22 | semidirect |
| 19. C2×#11745669 | C22 | semidirect |
| 20. C2×#11745659 | C22 | semidirect |
| 21. #14273727 | C22 | semidirect |
| 24. #14273707 | C22 | semidirect |
| 31. C4⋊(C59⋊C8) | C22 | semidirect |
| 32. #14273650 | C22 | semidirect |
| 33. #14273647 | C22 | semidirect |
| 34. (C2×D59)⋊C8 | C22 | semidirect |
| 37. C4×D4×C59 | C22 | semidirect |
| 38. #107×C59 | C22 | semidirect |
| 40. #102×C59 | C22 | semidirect |
| 41. C4×C8×C59 | C22 | semidirect |
| 62. D8×C59 | D4 | semidirect |
| 93. D4×C59 | C2×D4 | semidirect |
| 117. C8×C59 | C2×D4 | semidirect |
| 136. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 158. C4×D8 | D59 | semidirect |
| 160. C59 | #3272 | semidirect |
| 181. C4×D4 | C2×D59 | semidirect |
| 183. #107 | C2×D59 | semidirect |
| 188. #102 | C2×D59 | semidirect |
| 190. C4×C8 | C2×D59 | semidirect |
| 215. D8 | D236 | semidirect |
| 252. D4 | C2×D236 | semidirect |
| 267. C8 | C2×D236 | semidirect |
| 287. C4 | #14273751 | semidirect |