Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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. #17985731 | C2 | semidirect |
| 5. Q8⋊(C71⋊C8) | C2 | semidirect |
| 6. #17985729 | C2 | semidirect |
| 7. Q8⋊C8×C71 | C2 | semidirect |
| 30. Q8×D71 | C8 | semidirect |
| 60. Q8×C71 | C2×C8 | semidirect |
| 80. Dic142 | C2×C8 | semidirect |
| 104. D71 | Q8⋊C8 | direct (N × H) |
| 106. C71 | C2×Q8⋊C8 | semidirect |
| 113. Q8⋊C8 | D71 | direct (N × H) |
| 169. Q8 | C8×D71 | semidirect |