Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #16863146 | C2 | semidirect |
| 4. Q8⋊(C67⋊C8) | C2 | semidirect |
| 6. C8×C67⋊C8 | C2 | semidirect |
| 7. C8×Q8×C67 | C2 | semidirect |
| 25. #11761615 | C8 | direct (N × H) |
| 43. Q8×C67 | C2×C8 | semidirect |
| 56. C8×C67 | SD16 | semidirect |
| 60. C67⋊C8 | C2×C8 | semidirect |
| 78. C67 | C8×SD16 | semidirect |
| 79. C8×Q8 | D67 | semidirect |
| 121. Q8 | C8×D67 | semidirect |
| 138. C8 | #11761615 | direct (N × H) |