Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 2. #16863762 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863693 | C2 | semidirect |
| 5. #16863673 | C2 | semidirect |
| 6. #16863596 | C2 | semidirect |
| 7. #16863596 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 9. #16863494 | C2 | semidirect |
| 10. C4×#11761615 | C2 | semidirect |
| 11. #557×C67 | C2 | semidirect |
| 79. Q8×C67 | #41 | semidirect |
| 125. C67 | #3368 | semidirect |
| 126. #557 | D67 | semidirect |
| 204. Q8 | #11761629 | semidirect |