Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #16838200 | C2 | semidirect |
| 2. C2×#14273753 | C2 | semidirect |
| 3. #16838168 | C2 | semidirect |
| 4. #16837669 | C2 | semidirect |
| 5. #16837662 | C2 | semidirect |
| 6. #16837451 | C2 | semidirect |
| 7. #16837386 | C2 | semidirect |
| 8. C2×#14273644 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C59 | C2 | semidirect |
| 11. #14273758 | C22 | semidirect |
| 15. #14273753 | C22 | semidirect |
| 21. #14273733 | C22 | semidirect |
| 26. #14273663 | C22 | semidirect |
| 27. #14273646 | C22 | semidirect |
| 28. #14273644 | C22 | semidirect |
| 29. #14273644 | C22 | semidirect |
| 34. C2×SD16×C59 | C22 | semidirect |
| 35. C2×D8×C59 | C22 | semidirect |
| 150. C2×AGL(1,ℤ/8) | D59 | semidirect |
| 157. C59 | #3068 | semidirect |
| 171. C2×SD16 | C2×D59 | semidirect |
| 173. C2×D8 | C2×D59 | semidirect |