Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #19127433 | C2 | semidirect |
| 5. Q8⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127431 | C2 | semidirect |
| 7. Q8⋊C8×C83 | C2 | semidirect |
| 59. Q8×C83 | M16 | semidirect |
| 79. Dic166 | M16 | semidirect |
| 105. C83 | #1491 | semidirect |
| 112. Q8⋊C8 | D83 | semidirect |
| 167. Q8 | #13050573 | semidirect |