Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #19127523 | C2 | semidirect |
| 4. #19127517 | C2 | semidirect |
| 6. #19127479 | C2 | semidirect |
| 7. #441×C83 | C2 | semidirect |
| 10. #14581738 | C4 | semidirect |
| 11. #14581735 | C4 | semidirect |
| 65. C83 | #2180 | semidirect |
| 68. #441 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128142 | 2 |
| #19127824 | 2 |
| #19127523 | 2 |
| #19127517 | 2 |
| #19127510 | 2 |
| #19127479 | 2 |
| #441×C83 | 2 |
| #2180 | 83 |