Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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. #16840598 | C2 | semidirect |
| 2. #16840573 | C2 | semidirect |
| 3. #16840565 | C2 | semidirect |
| 4. #16840560 | C2 | semidirect |
| 5. C2×#14519803 | C2 | semidirect |
| 6. #16840529 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C61 | C2 | semidirect |
| 9. #14519824 | C22 | semidirect |
| 10. #14519823 | C22 | semidirect |
| 12. C2×#11758222 | C22 | semidirect |
| 14. #14519808 | C22 | semidirect |
| 15. #14519807 | C22 | semidirect |
| 16. #14519803 | C22 | semidirect |
| 17. #14519803 | C22 | semidirect |
| 18. #14519802 | C22 | semidirect |
| 19. #14519797 | C22 | semidirect |
| 20. C2×#11758200 | C22 | semidirect |
| 21. C2×#11758199 | C22 | semidirect |
| 22. #14519784 | C22 | semidirect |
| 23. C2×#11758194 | C22 | semidirect |
| 25. H(5,𝔽2)×C61 | C22 | semidirect |
| 28. C2×#41×C61 | C22 | semidirect |
| 30. C22×D4×C61 | C22 | semidirect |
| 56. #11758222 | C23 | semidirect |
| 57. C2×D244 | C23 | semidirect |
| 59. C2×Dic122 | C23 | semidirect |
| 60. #11758202 | C23 | semidirect |
| 61. #11758201 | C23 | semidirect |
| 62. #11758200 | C23 | semidirect |
| 63. #11758199 | C23 | semidirect |
| 65. #11758194 | C23 | semidirect |
| 66. C2×#92418 | C23 | semidirect |
| 116. C2×H(5,𝔽2) | D61 | semidirect |
| 122. C61 | #3585 | semidirect |
| 128. H(5,𝔽2) | C2×D61 | semidirect |
| 133. C2×#41 | C2×D61 | semidirect |
| 135. C22×D4 | C2×D61 | semidirect |