Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4⋊Q8×D83 | C2 | semidirect |
| 3. #19128063 | C2 | semidirect |
| 4. #19128061 | C2 | semidirect |
| 5. #19128060 | C2 | semidirect |
| 6. #19128050 | C2 | semidirect |
| 7. #19128046 | C2 | semidirect |
| 8. #19127701 | C2 | semidirect |
| 9. #19127699 | C2 | semidirect |
| 10. #19127653 | C2 | semidirect |
| 11. #489×C83 | C2 | semidirect |
| 141. C83 | #3141 | semidirect |
| 147. #489 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128250 | 2 |
| C4⋊Q8×D83 | 2 |
| #19128063 | 2 |
| #19128061 | 2 |
| #19128060 | 2 |
| #19128050 | 2 |
| #19128046 | 2 |
| #19127701 | 2 |
| #19127699 | 2 |
| #19127653 | 2 |
| #489×C83 | 2 |
| #3141 | 83 |