Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D83 | C2 | semidirect |
| 3. #19127994 | C2 | semidirect |
| 4. #19127990 | C2 | semidirect |
| 5. #19127986 | C2 | semidirect |
| 6. #19127982 | C2 | semidirect |
| 7. #19127978 | C2 | semidirect |
| 8. #19127740 | C2 | semidirect |
| 9. #19127723 | C2 | semidirect |
| 11. #475×C83 | C2 | semidirect |
| 44. #13050591 | Q8 | semidirect |
| 86. Q8×C83 | C2×Q8 | semidirect |
| 100. D332 | C2×Q8 | semidirect |
| 138. C83 | #3079 | semidirect |
| 144. #475 | D83 | semidirect |
| 226. Q8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D83 | 2 |
| C4×#13050591 | 2 |
| #19127994 | 2 |
| #19127990 | 2 |
| #19127986 | 2 |
| #19127982 | 2 |
| #19127978 | 2 |
| #19127740 | 2 |
| #19127723 | 2 |
| #19127701 | 2 |
| #475×C83 | 2 |
| #3079 | 83 |