Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11745660 | C2 | semidirect |
| 2. C22×#11745670 | C2 | semidirect |
| 3. C22×#11745669 | C2 | semidirect |
| 4. C2×#14273723 | C2 | semidirect |
| 5. C2×#14273714 | C2 | semidirect |
| 6. #16837790 | C2 | direct (N × H) |
| 7. C2×#14273637 | C2 | semidirect |
| 8. C22×D8×C59 | C2 | semidirect |
| 13. C2×#11745660 | C22 | semidirect |
| 15. C2×#11745670 | C22 | semidirect |
| 17. C2×#11745669 | C22 | semidirect |
| 20. #14273723 | C22 | semidirect |
| 22. #14273714 | C22 | semidirect |
| 25. #14273637 | C22 | semidirect |
| 29. C2×D8×C59 | C22 | semidirect |
| 56. C2×C8×C59 | D4 | semidirect |
| 63. C2×C59⋊C8 | D4 | semidirect |
| 97. C8×C59 | C2×D4 | semidirect |
| 98. C59⋊C8 | C2×D4 | semidirect |
| 119. C2×C59 | #496 | semidirect |
| 126. C22×D8 | D59 | semidirect |
| 131. C59 | C2×#496 | semidirect |
| 144. C2×D8 | C2×D59 | semidirect |
| 184. C2×C8 | C22⋊D59 | semidirect |
| 221. C8 | C2×C22⋊D59 | semidirect |
| 242. C2 | #16837790 | direct (N × H) |