Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864119 | C2 | semidirect |
| 2. #16863753 | C2 | semidirect |
| 3. #16863748 | C2 | semidirect |
| 4. #16863700 | C2 | semidirect |
| 5. #16863683 | C2 | semidirect |
| 7. #16863601 | C2 | semidirect |
| 8. Q8×C67⋊C8 | C2 | semidirect |
| 9. C4×#11761616 | C2 | semidirect |
| 11. #554×C67 | C2 | semidirect |
| 121. C67 | #3360 | semidirect |
| 123. #554 | D67 | semidirect |