Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128322 | C2 | semidirect |
| 2. #19128099 | C2 | semidirect |
| 3. #19128085 | C2 | semidirect |
| 4. #19128061 | C2 | semidirect |
| 5. #19127959 | C2 | semidirect |
| 7. #19127930 | C2 | semidirect |
| 8. #19127814 | C2 | semidirect |
| 9. #19127809 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. #405×C83 | C2 | semidirect |
| 110. C83 | #3173 | semidirect |
| 121. #405 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128322 | 2 |
| #19128099 | 2 |
| #19128085 | 2 |
| #19128061 | 2 |
| #19127959 | 2 |
| #19127954 | 2 |
| #19127930 | 2 |
| #19127814 | 2 |
| #19127809 | 2 |
| C4×#13050579 | 2 |
| #405×C83 | 2 |
| #3173 | 83 |