Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19128329 | C2 | semidirect |
| 3. #19128003 | C2 | semidirect |
| 4. #19127999 | C2 | semidirect |
| 5. #19127989 | C2 | semidirect |
| 6. #19127979 | C2 | semidirect |
| 7. #19127743 | C2 | semidirect |
| 8. #19127737 | C2 | semidirect |
| 9. #19127729 | C2 | semidirect |
| 14. #14581791 | C22 | semidirect |
| 16. #14581783 | C22 | semidirect |
| 26. #14581726 | C22 | semidirect |
| 27. #14581725 | C22 | semidirect |
| 28. #14581725 | C22 | semidirect |
| 29. #14581724 | C22 | semidirect |
| 30. #14581723 | C22 | semidirect |
| 31. #14581723 | C22 | semidirect |
| 32. Dic83⋊C8 | C22 | semidirect |
| 33. Dic83⋊C8 | C22 | semidirect |
| 66. C2×D4×C83 | Q8 | semidirect |
| 125. C83 | #3081 | semidirect |
| 170. C2×D4 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128176 | 2 |
| #19128003 | 2 |
| #19127999 | 2 |
| #19127989 | 2 |
| #19127979 | 2 |
| #19127743 | 2 |
| #19127737 | 2 |
| #19127729 | 2 |
| C2×#14581713 | 2 |
| #418×C83 | 2 |
| #3081 | 83 |