Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 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×SD16×D59 | C2 | semidirect |
| 2. Q8×D236 | C2 | semidirect |
| 4. #16837775 | C2 | semidirect |
| 5. #16837632 | C2 | semidirect |
| 6. #16837607 | C2 | semidirect |
| 7. #16837602 | C2 | semidirect |
| 8. #16837554 | C2 | semidirect |
| 9. #16837542 | C2 | semidirect |
| 10. C8×D236 | C2 | semidirect |
| 11. C4×SD16×C59 | C2 | semidirect |
| 12. C2×Q8×D59 | C22 | semidirect |
| 15. C2×#11745660 | C22 | semidirect |
| 16. C2×#11745660 | C22 | semidirect |
| 18. C2×#11745671 | C22 | semidirect |
| 20. C2×C8×D59 | C22 | semidirect |
| 22. #14273727 | C22 | semidirect |
| 25. #14273707 | C22 | semidirect |
| 31. C4⋊(C59⋊C8) | C22 | semidirect |
| 32. #14273650 | C22 | semidirect |
| 33. #14273647 | C22 | semidirect |
| 34. (C2×D59)⋊C8 | C22 | semidirect |
| 36. C4×Q8×C59 | C22 | semidirect |
| 38. #106×C59 | C22 | semidirect |
| 39. #103×C59 | C22 | semidirect |
| 41. C4×C8×C59 | C22 | semidirect |
| 61. SD16×C59 | D4 | semidirect |
| 90. Q8×C59 | C2×D4 | semidirect |
| 108. D236 | SD16 | direct (N × H) |
| 116. C8×C59 | C2×D4 | semidirect |
| 128. C2×D59 | C2×SD16 | semidirect |
| 133. C4×C59 | C2×SD16 | semidirect |
| 154. C4×SD16 | D59 | semidirect |
| 156. C59 | D4×SD16 | semidirect |
| 175. C4×Q8 | C2×D59 | semidirect |
| 179. #106 | C2×D59 | semidirect |
| 182. #103 | C2×D59 | semidirect |
| 186. C4×C8 | C2×D59 | semidirect |
| 210. SD16 | D236 | direct (N × H) |
| 238. Q8 | C2×D236 | semidirect |
| 262. C8 | C2×D236 | semidirect |
| 280. C4 | SD16×D59 | semidirect |