Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273752 | C2 | semidirect |
| 2. C22×#11745669 | C2 | semidirect |
| 3. C2×#14273734 | C2 | semidirect |
| 4. #16837670 | C2 | direct (N × H) |
| 5. C2×#14273662 | C2 | semidirect |
| 6. C2×#14273644 | C2 | semidirect |
| 7. C2×#14273643 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C59 | C2 | semidirect |
| 11. #14273752 | C22 | semidirect |
| 17. C2×#11745669 | C22 | semidirect |
| 19. #14273734 | C22 | semidirect |
| 25. #14273662 | C22 | semidirect |
| 26. #14273644 | C22 | semidirect |
| 27. #14273643 | C22 | semidirect |
| 31. AGL(1,ℤ/8)×C59 | C22 | semidirect |
| 141. C2×C59 | #472 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D59 | semidirect |
| 152. C59 | C2×#472 | semidirect |
| 159. AGL(1,ℤ/8) | C2×D59 | semidirect |
| 285. C2 | #16837670 | direct (N × H) |