Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#14273734 | C2 | semidirect |
| 2. #16837885 | C2 | semidirect |
| 3. #16837407 | C2 | semidirect |
| 4. #16837403 | C2 | semidirect |
| 5. #16837398 | C2 | semidirect |
| 6. C2×#14273648 | C2 | semidirect |
| 9. C2×#11745664 | C22 | semidirect |
| 10. C22×C59⋊C8 | C22 | semidirect |
| 13. #14273686 | C22 | semidirect |
| 14. C2×C4⋊Dic59 | C22 | semidirect |
| 15. #14273651 | C22 | semidirect |
| 16. #14273651 | C22 | semidirect |
| 17. #14273648 | C22 | semidirect |
| 18. #14273648 | C22 | semidirect |
| 19. #14273648 | C22 | semidirect |
| 21. H(5,𝔽2)×C59 | C4 | semidirect |
| 31. #41×C59 | C2×C4 | semidirect |
| 39. C2×D4×C59 | C2×C4 | semidirect |
| 105. C59 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic59 | semidirect |
| 129. #41 | C2×Dic59 | semidirect |
| 137. C2×D4 | C2×Dic59 | semidirect |