Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C4×Q8×D83 | C2 | semidirect |
| 4. #19127926 | C2 | semidirect |
| 5. #19127925 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 7. #19127902 | C2 | semidirect |
| 8. #19127901 | C2 | semidirect |
| 9. #19127723 | C2 | semidirect |
| 10. #19127701 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 49. Q8×D83 | D4 | semidirect |
| 133. C4×C83 | #137 | semidirect |
| 147. C83 | #3037 | semidirect |
| 154. #462 | D83 | semidirect |
| 285. 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 |
| #19128252 | 2 |
| C4×Q8×D83 | 2 |
| #19127926 | 2 |
| #19127925 | 2 |
| #19127908 | 2 |
| #19127902 | 2 |
| #19127901 | 2 |
| #19127723 | 2 |
| #19127701 | 2 |
| #462×C83 | 2 |
| #3037 | 83 |