Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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. C2×#14581824 | C2 | semidirect |
| 3. #19128366 | C2 | semidirect |
| 4. #19128075 | C2 | semidirect |
| 5. #19127950 | C2 | semidirect |
| 6. #19127902 | C2 | semidirect |
| 7. #19127862 | C2 | semidirect |
| 8. #19127841 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 10. #19127778 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 57. #13050580 | D4 | semidirect |
| 125. C4×C83 | #137 | semidirect |
| 137. C83 | #3278 | semidirect |
| 143. #462 | D83 | semidirect |
| 265. C4 | #14581824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581824 | 2 |
| #19128373 | 2 |
| #19128366 | 2 |
| #19128075 | 2 |
| #19127950 | 2 |
| #19127902 | 2 |
| #19127862 | 2 |
| #19127841 | 2 |
| C4×#13050580 | 2 |
| #19127778 | 2 |
| #462×C83 | 2 |
| #3278 | 83 |