Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic134 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863741 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863685 | C2 | semidirect |
| 7. #16863596 | C2 | semidirect |
| 8. #16863594 | C2 | semidirect |
| 9. C8×Dic134 | C2 | semidirect |
| 10. #16863481 | C2 | semidirect |
| 11. C4×SD16×C67 | C2 | semidirect |
| 77. Q8×C67 | #41 | semidirect |
| 99. Dic134 | SD16 | semidirect |
| 126. C67 | #3362 | semidirect |
| 137. C4×SD16 | D67 | semidirect |
| 206. Q8 | #11761628 | semidirect |