Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D83 | C2 | semidirect |
| 2. #19128336 | C2 | semidirect |
| 3. #19127934 | C2 | semidirect |
| 4. #19127893 | C2 | semidirect |
| 5. #19127833 | C2 | semidirect |
| 6. C4×D664 | C2 | semidirect |
| 7. C8×D332 | C2 | semidirect |
| 8. #493×C83 | C2 | semidirect |
| 10. C2×D4×D83 | C22 | semidirect |
| 12. C2×#13050575 | C22 | semidirect |
| 14. C2×C8×D83 | C22 | semidirect |
| 16. #14581763 | C22 | semidirect |
| 19. C4×D332 | C22 | semidirect |
| 20. #14581726 | C22 | semidirect |
| 21. C4⋊(C83⋊C8) | C22 | semidirect |
| 22. #14581714 | C22 | semidirect |
| 23. #14581713 | C22 | semidirect |
| 24. (C2×D83)⋊C8 | C22 | semidirect |
| 25. C2×D8×C83 | C22 | semidirect |
| 26. C2×D8×C83 | C22 | semidirect |
| 27. #127×C83 | C22 | semidirect |
| 28. C4×C8×C83 | C22 | semidirect |
| 39. D664 | D4 | semidirect |
| 74. D332 | D8 | semidirect |
| 75. D332 | C2×D4 | semidirect |
| 80. C8×C83 | C2×D4 | semidirect |
| 92. C2×D83 | C2×D8 | semidirect |
| 94. C4×C83 | C2×D8 | semidirect |
| 106. C83 | D4×D8 | semidirect |
| 109. #493 | D83 | semidirect |
| 120. C2×D8 | C2×D83 | semidirect |
| 121. C2×D8 | C2×D83 | semidirect |
| 123. #127 | C2×D83 | semidirect |
| 134. C4×C8 | C2×D83 | semidirect |
| 187. C8 | D4×D83 | semidirect |
| 202. C4 | D8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D83 | 2 |
| #19128336 | 2 |
| #19127934 | 2 |
| #19127893 | 2 |
| #19127833 | 2 |
| C4×D664 | 2 |
| C8×D332 | 2 |
| #493×C83 | 2 |
| D4×D8 | 83 |