Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 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. #19128436 | C2 | semidirect |
| 2. #19128063 | C2 | semidirect |
| 3. #19128049 | C2 | semidirect |
| 4. #19127988 | C2 | semidirect |
| 5. #19127983 | C2 | semidirect |
| 6. #19127916 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 9. #19127811 | C2 | semidirect |
| 10. C4×#13050578 | C2 | semidirect |
| 11. D4×Q8×C83 | C2 | semidirect |
| 125. C83 | #3373 | semidirect |
| 127. D4×Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128436 | 2 |
| #19128063 | 2 |
| #19128049 | 2 |
| #19127988 | 2 |
| #19127983 | 2 |
| #19127916 | 2 |
| #19127896 | 2 |
| #19127832 | 2 |
| #19127811 | 2 |
| C4×#13050578 | 2 |
| D4×Q8×C83 | 2 |
| #3373 | 83 |