Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128238 | C2 | semidirect |
| 2. #19128101 | C2 | semidirect |
| 3. #19128086 | C2 | semidirect |
| 4. #19128057 | C2 | semidirect |
| 5. #19127956 | C2 | semidirect |
| 7. #19127950 | C2 | semidirect |
| 8. #19127814 | C2 | semidirect |
| 9. #19127799 | C2 | semidirect |
| 10. #19127653 | C2 | semidirect |
| 11. #441×C83 | C2 | semidirect |
| 110. C83 | #3183 | semidirect |
| 119. #441 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128238 | 2 |
| #19128101 | 2 |
| #19128086 | 2 |
| #19128057 | 2 |
| #19127956 | 2 |
| #19127955 | 2 |
| #19127950 | 2 |
| #19127814 | 2 |
| #19127799 | 2 |
| #19127653 | 2 |
| #441×C83 | 2 |
| #3183 | 83 |