Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 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. C2×#14273752 | C2 | semidirect |
| 2. C22×#11745669 | C2 | semidirect |
| 3. #16837966 | C2 | semidirect |
| 4. #16837547 | C2 | semidirect |
| 5. #16837536 | C2 | semidirect |
| 6. #16837407 | C2 | semidirect |
| 7. #16837398 | C2 | semidirect |
| 8. #16837369 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C59 | C2 | semidirect |
| 10. C22×D236 | C22 | semidirect |
| 12. C2×#11745671 | C22 | semidirect |
| 14. C2×#11745669 | C22 | semidirect |
| 15. C2×#11745669 | C22 | semidirect |
| 16. C2×#11745664 | C22 | semidirect |
| 17. C22×C59⋊C8 | C22 | semidirect |
| 20. #14273701 | C22 | semidirect |
| 22. #14273686 | C22 | semidirect |
| 23. #14273651 | C22 | semidirect |
| 24. #14273648 | C22 | semidirect |
| 25. #14273648 | C22 | semidirect |
| 26. C22⋊(C59⋊C8) | C22 | semidirect |
| 32. C2×#41×C59 | C22 | semidirect |
| 36. C22×D4×C59 | C22 | semidirect |
| 46. #41×C59 | D4 | semidirect |
| 60. C2×D4×C59 | D4 | semidirect |
| 152. C2×H(5,𝔽2) | D59 | semidirect |
| 161. C59 | #3008 | semidirect |
| 167. C2×#41 | C2×D59 | semidirect |
| 172. C22×D4 | C2×D59 | semidirect |
| 198. #41 | C22⋊D59 | semidirect |
| 217. C2×D4 | C22⋊D59 | semidirect |