Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 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. C2×#14273706 | C2 | semidirect |
| 4. #16837648 | C2 | direct (N × H) |
| 5. C2×#14273661 | C2 | semidirect |
| 6. C2×#14273652 | C2 | semidirect |
| 7. C2×#14273649 | C2 | semidirect |
| 8. C22×M16×C59 | C2 | semidirect |
| 13. C2×#11745660 | C22 | semidirect |
| 15. #14273706 | C22 | semidirect |
| 23. #14273661 | C22 | semidirect |
| 24. #14273652 | C22 | semidirect |
| 25. #14273649 | C22 | semidirect |
| 28. C2×M16×C59 | C22 | semidirect |
| 54. C2×C8×C59 | D4 | semidirect |
| 97. C8×C59 | C2×D4 | semidirect |
| 119. C2×C59 | #468 | semidirect |
| 125. C22×M16 | D59 | semidirect |
| 132. C59 | C2×#468 | semidirect |
| 140. C2×M16 | C2×D59 | semidirect |
| 179. C2×C8 | C22⋊D59 | semidirect |
| 221. C8 | C2×C22⋊D59 | semidirect |
| 243. C2 | #16837648 | direct (N × H) |