Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×Q16×D83 | C2 | semidirect |
| 4. #19128080 | C2 | semidirect |
| 5. #19127941 | C2 | semidirect |
| 6. #19127912 | C2 | semidirect |
| 7. #19127858 | C2 | semidirect |
| 8. #19127855 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 57. #13050580 | D4 | semidirect |
| 97. D332 | Q16 | semidirect |
| 114. C2×D83 | C2×Q16 | semidirect |
| 119. C4×C83 | C2×Q16 | semidirect |
| 131. C83 | D4×Q16 | semidirect |
| 138. #462 | D83 | semidirect |
| 254. C4 | Q16×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D83 | 2 |
| Q8×D332 | 2 |
| #19128366 | 2 |
| #19128080 | 2 |
| #19127941 | 2 |
| #19127912 | 2 |
| #19127858 | 2 |
| #19127855 | 2 |
| C4×#13050580 | 2 |
| #19127766 | 2 |
| #462×C83 | 2 |
| D4×Q16 | 83 |