Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C2×#14273686 | C2 | semidirect |
| 3. #16837408 | C2 | direct (N × H) |
| 4. C2×#14273649 | C2 | semidirect |
| 5. C22×M16×C59 | C2 | semidirect |
| 10. C22×D236 | C4 | semidirect |
| 14. #14273686 | C22 | semidirect |
| 15. C2×C4⋊Dic59 | C22 | semidirect |
| 18. #14273649 | C22 | semidirect |
| 21. C2×M16×C59 | C22 | semidirect |
| 22. C22×C8×C59 | C22 | semidirect |
| 42. C2×D236 | C2×C4 | semidirect |
| 46. C2×C8×C59 | C23 | semidirect |
| 49. C4⋊Dic59 | C23 | semidirect |
| 94. C2×C59 | #418 | semidirect |
| 99. C22×M16 | D59 | semidirect |
| 103. C59 | C2×#418 | semidirect |
| 113. C2×M16 | C2×D59 | semidirect |
| 114. C22×C8 | C2×D59 | semidirect |
| 144. C2×C8 | C22×D59 | semidirect |
| 192. C2 | #16837408 | direct (N × H) |