Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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. #16863527 | C2 | semidirect |
| 4. #16863148 | C2 | semidirect |
| 6. #16863118 | C2 | semidirect |
| 7. Q8⋊C8×C67 | C2 | semidirect |
| 60. C67⋊C8 | M16 | semidirect |
| 78. C67 | #1592 | semidirect |
| 83. Q8⋊C8 | D67 | semidirect |