Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 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. C2×#14581751 | C2 | semidirect |
| 2. #19128022 | C2 | semidirect |
| 3. #19128017 | C2 | semidirect |
| 4. #19128012 | C2 | semidirect |
| 5. #19127741 | C2 | semidirect |
| 6. #19127706 | C2 | semidirect |
| 7. #19127665 | C2 | semidirect |
| 13. #14581751 | C22 | semidirect |
| 14. C2×C4⋊Dic83 | C22 | semidirect |
| 15. C2×C4⋊Dic83 | C22 | semidirect |
| 18. #14581725 | C22 | semidirect |
| 19. #14581723 | C22 | semidirect |
| 20. #14581713 | C22 | semidirect |
| 21. #14581713 | C22 | semidirect |
| 22. C22⋊(C83⋊C8) | C22 | semidirect |
| 23. C22⋊(C83⋊C8) | C22 | semidirect |
| 126. C83 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581751 | 2 |
| #19128022 | 2 |
| #19128017 | 2 |
| #19128012 | 2 |
| #19127741 | 2 |
| #19127706 | 2 |
| #19127665 | 2 |
| C2×#121×C83 | 2 |
| #3094 | 83 |