Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
446 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128252 | C2 | semidirect |
| 2. #19128249 | C2 | semidirect |
| 3. #19128097 | C2 | semidirect |
| 4. #19128077 | C2 | semidirect |
| 5. #19128048 | C2 | semidirect |
| 6. #19127953 | C2 | semidirect |
| 7. #19127810 | C2 | semidirect |
| 8. C4×#13050573 | C2 | semidirect |
| 9. #486×C83 | C2 | semidirect |
| 95. C83⋊C8 | #41 | semidirect |
| 121. C83 | #3184 | semidirect |
| 127. #486 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128249 | 2 |
| #19128097 | 2 |
| #19128077 | 2 |
| #19128048 | 2 |
| #19127953 | 2 |
| #19127810 | 2 |
| C4×#13050573 | 2 |
| #486×C83 | 2 |
| #3184 | 83 |