Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14581823 | C2 | semidirect |
| 2. C2×#14581822 | C2 | semidirect |
| 4. C22×#13050580 | C2 | semidirect |
| 5. #19128277 | C2 | semidirect |
| 6. #19128096 | C2 | semidirect |
| 7. #19128093 | C2 | semidirect |
| 8. #19128083 | C2 | semidirect |
| 9. #19128080 | C2 | semidirect |
| 10. #19127657 | C2 | semidirect |
| 11. #536×C83 | C2 | semidirect |
| 144. C83 | #3156 | semidirect |
| 150. #536 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| C2×#14581822 | 2 |
| C2×#14581812 | 2 |
| C22×#13050580 | 2 |
| #19128277 | 2 |
| #19128096 | 2 |
| #19128093 | 2 |
| #19128083 | 2 |
| #19128080 | 2 |
| #19127657 | 2 |
| #536×C83 | 2 |
| #3156 | 83 |