Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14273715 | C2 | semidirect |
| 2. #16837789 | C2 | semidirect |
| 3. #16837764 | C2 | semidirect |
| 4. #16837617 | C2 | semidirect |
| 5. #16837540 | C2 | semidirect |
| 6. #16837535 | C2 | semidirect |
| 7. #16837459 | C2 | semidirect |
| 8. C59×#532 | C2 | semidirect |
| 11. C2×#11745670 | C22 | semidirect |
| 19. C4⋊(C59⋊C8) | C22 | semidirect |
| 20. #14273650 | C22 | semidirect |
| 23. #14273638 | C22 | semidirect |
| 25. C4⋊Q8×C59 | C22 | semidirect |
| 26. #127×C59 | C22 | semidirect |
| 31. C4×D4×C59 | C22 | semidirect |
| 121. #532 | D59 | semidirect |
| 129. C59 | #3213 | semidirect |
| 135. C4⋊Q8 | C2×D59 | semidirect |
| 136. #127 | C2×D59 | semidirect |
| 145. C4×D4 | C2×D59 | semidirect |