Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. C2×#14581757 | C2 | semidirect |
| 3. #19128014 | C2 | semidirect |
| 4. #19127995 | C2 | semidirect |
| 5. #19127900 | C2 | semidirect |
| 6. #19127842 | C2 | semidirect |
| 7. #19127839 | C2 | semidirect |
| 8. #19127800 | C2 | semidirect |
| 9. #19127798 | C2 | semidirect |
| 10. #19127755 | C2 | semidirect |
| 11. #480×C83 | C2 | semidirect |
| 111. Dic166 | #41 | semidirect |
| 141. C83 | #3112 | semidirect |
| 145. #480 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128246 | 2 |
| C2×#14581757 | 2 |
| #19128014 | 2 |
| #19127995 | 2 |
| #19127900 | 2 |
| #19127842 | 2 |
| #19127839 | 2 |
| #19127800 | 2 |
| #19127798 | 2 |
| #19127755 | 2 |
| #480×C83 | 2 |
| #3112 | 83 |