Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 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. C22×#13050575 | C2 | semidirect |
| 2. C2×#14581800 | C2 | semidirect |
| 3. #19128270 | C2 | semidirect |
| 4. #19128268 | C2 | semidirect |
| 5. #19127953 | C2 | semidirect |
| 6. #19127936 | C2 | semidirect |
| 7. #19127737 | C2 | semidirect |
| 8. #19127707 | C2 | semidirect |
| 9. #418×C83 | C2 | semidirect |
| 16. C2×#13050573 | C22 | semidirect |
| 18. C2×C8×D83 | C22 | semidirect |
| 23. #14581767 | C22 | semidirect |
| 24. #14581763 | C22 | semidirect |
| 28. #14581725 | C22 | semidirect |
| 29. #14581723 | C22 | semidirect |
| 30. #14581714 | C22 | semidirect |
| 34. #102×C83 | C22 | semidirect |
| 51. C2×C83⋊C8 | D4 | semidirect |
| 126. C83 | #3058 | semidirect |
| 135. #418 | D83 | semidirect |
| 160. #102 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050575 | 2 |
| C2×#14581800 | 2 |
| #19128270 | 2 |
| #19128268 | 2 |
| #19127953 | 2 |
| #19127936 | 2 |
| #19127737 | 2 |
| #19127707 | 2 |
| #418×C83 | 2 |
| #3058 | 83 |