Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128411 | C2 | semidirect |
| 3. #19128048 | C2 | semidirect |
| 4. #19128016 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 6. #19127950 | C2 | semidirect |
| 7. #19127901 | C2 | semidirect |
| 8. #19127862 | C2 | semidirect |
| 9. #19127780 | C2 | semidirect |
| 10. #19127701 | C2 | semidirect |
| 11. C4×Q16×C83 | C2 | semidirect |
| 129. C83 | #3333 | semidirect |
| 138. C4×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| #19128373 | 2 |
| #19128048 | 2 |
| #19128016 | 2 |
| #19127996 | 2 |
| #19127950 | 2 |
| #19127901 | 2 |
| #19127862 | 2 |
| #19127780 | 2 |
| #19127701 | 2 |
| C4×Q16×C83 | 2 |
| #3333 | 83 |