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×#14273752 | C2 | semidirect |
| 2. D4×D236 | C2 | semidirect |
| 3. #16837776 | C2 | semidirect |
| 4. #16837650 | C2 | semidirect |
| 5. #16837604 | C2 | semidirect |
| 6. #16837597 | C2 | semidirect |
| 7. #16837552 | C2 | semidirect |
| 8. #16837547 | C2 | semidirect |
| 9. C4×#11745669 | C2 | semidirect |
| 10. #16837480 | C2 | semidirect |
| 11. C59×#547 | C2 | semidirect |
| 16. C2×#11745671 | C22 | semidirect |
| 17. C2×#11745671 | C22 | semidirect |
| 19. C2×#11745669 | C22 | semidirect |
| 20. C2×#11745664 | C22 | semidirect |
| 26. #14273660 | C22 | semidirect |
| 27. C4⋊(C59⋊C8) | C22 | semidirect |
| 28. #14273651 | C22 | semidirect |
| 29. #14273648 | C22 | semidirect |
| 31. #14273647 | C22 | semidirect |
| 32. C22⋊(C59⋊C8) | C22 | semidirect |
| 33. C4×C59⋊C8 | C22 | semidirect |
| 34. C2×#41×C59 | C22 | semidirect |
| 35. C4⋊Q8×C59 | C22 | semidirect |
| 37. C22⋊Q8×C59 | C22 | semidirect |
| 40. C4×D4×C59 | C22 | semidirect |
| 75. #11745669 | D4 | semidirect |
| 95. D4×C59 | C2×D4 | semidirect |
| 118. C59⋊C8 | C2×D4 | semidirect |
| 137. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 150. #547 | D59 | semidirect |
| 160. C59 | #3272 | semidirect |
| 161. C2×#41 | C2×D59 | semidirect |
| 171. C4⋊Q8 | C2×D59 | semidirect |
| 174. C22⋊Q8 | C2×D59 | semidirect |
| 181. C4×D4 | C2×D59 | semidirect |
| 252. D4 | D4×D59 | semidirect |
| 287. C4 | #14273752 | semidirect |