Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#14273724 | C2 | semidirect |
| 3. #16837792 | C2 | semidirect |
| 4. #16837778 | C2 | semidirect |
| 5. #16837776 | C2 | semidirect |
| 6. C4×#11745664 | C2 | semidirect |
| 7. C59×#532 | C2 | semidirect |
| 11. C2×#11745671 | C22 | semidirect |
| 12. C2×#11745669 | C22 | semidirect |
| 17. #14273638 | C22 | semidirect |
| 18. C4×C59⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C59 | C22 | semidirect |
| 21. #127×C59 | C22 | semidirect |
| 22. #124×C59 | C22 | semidirect |
| 48. #11745664 | D4 | semidirect |
| 71. C59⋊C8 | C2×D4 | semidirect |
| 83. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 92. #532 | D59 | semidirect |
| 98. C59 | #3151 | semidirect |
| 106. C4⋊Q8 | C2×D59 | semidirect |
| 110. #127 | C2×D59 | semidirect |
| 111. #124 | C2×D59 | semidirect |
| 174. C4 | #14273752 | semidirect |