Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14273774 | C2 | semidirect |
| 2. #16838200 | C2 | semidirect |
| 3. #16837973 | C2 | semidirect |
| 4. #16837583 | C2 | semidirect |
| 5. #16837573 | C2 | semidirect |
| 6. #16837419 | C2 | semidirect |
| 7. #16837418 | C2 | semidirect |
| 8. C2×#14273645 | C2 | semidirect |
| 9. C59×#575 | C2 | semidirect |
| 21. #14273758 | C22 | semidirect |
| 23. #14273753 | C22 | semidirect |
| 27. #14273725 | C22 | semidirect |
| 28. #14273714 | C22 | semidirect |
| 32. #14273654 | C22 | semidirect |
| 33. #14273653 | C22 | semidirect |
| 34. #14273645 | C22 | semidirect |
| 38. #137×C59 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C59 | C22 | semidirect |
| 188. #575 | D59 | semidirect |
| 195. C59 | #3020 | semidirect |
| 212. #137 | C2×D59 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D59 | semidirect |