Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
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. D4×D236 | C2 | semidirect |
| 2. #16837750 | C2 | semidirect |
| 3. #16837715 | C2 | semidirect |
| 4. #16837679 | C2 | semidirect |
| 5. #16837636 | C2 | semidirect |
| 6. #16837597 | C2 | semidirect |
| 7. #16837535 | C2 | semidirect |
| 8. C4×#11745669 | C2 | semidirect |
| 9. D4×C59⋊C8 | C2 | semidirect |
| 10. C2×#14273647 | C2 | semidirect |
| 11. C59×#547 | C2 | semidirect |
| 15. C2×#11745669 | C22 | semidirect |
| 16. C22×C59⋊C8 | C22 | semidirect |
| 22. #14273660 | C22 | semidirect |
| 23. #14273660 | C22 | semidirect |
| 24. C4⋊(C59⋊C8) | C22 | semidirect |
| 25. #14273648 | C22 | semidirect |
| 28. #14273647 | C22 | semidirect |
| 29. #14273647 | C22 | semidirect |
| 30. #14273647 | C22 | semidirect |
| 31. C22⋊(C59⋊C8) | C22 | semidirect |
| 32. C4×C59⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C59 | C22 | semidirect |
| 37. #121×C59 | C22 | semidirect |
| 39. C4×D4×C59 | C22 | semidirect |
| 40. C2×C4⋊C4×C59 | C22 | semidirect |
| 89. D4×C59 | D8 | semidirect |
| 108. D236 | #41 | semidirect |
| 143. #547 | D59 | semidirect |
| 154. C59 | #3294 | semidirect |
| 161. C4⋊Q8 | C2×D59 | semidirect |
| 167. #121 | C2×D59 | semidirect |
| 171. C4×D4 | C2×D59 | semidirect |
| 172. C2×C4⋊C4 | C2×D59 | semidirect |
| 240. D4 | #11745669 | semidirect |