Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D268 | C2 | semidirect |
| 2. #16863755 | C2 | semidirect |
| 3. #16863742 | C2 | semidirect |
| 4. #16863686 | C2 | semidirect |
| 5. #16863681 | C2 | semidirect |
| 6. #16863608 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 9. #16863506 | C2 | semidirect |
| 10. C4×#11761615 | C2 | semidirect |
| 11. #559×C67 | C2 | semidirect |
| 125. C67 | #3373 | semidirect |
| 126. #559 | D67 | semidirect |