Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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. #16863941 | C2 | semidirect |
| 2. #16863793 | C2 | semidirect |
| 3. #16863771 | C2 | semidirect |
| 4. #16863741 | C2 | semidirect |
| 5. #16863649 | C2 | semidirect |
| 6. #16863647 | C2 | semidirect |
| 7. #16863508 | C2 | semidirect |
| 8. #16863507 | C2 | semidirect |
| 9. #16863505 | C2 | semidirect |
| 10. M16×Dic67 | C2 | semidirect |
| 11. #469×C67 | C2 | semidirect |
| 94. C8×C67 | #41 | semidirect |
| 96. C67⋊C8 | #41 | semidirect |
| 119. C67 | #3184 | semidirect |
| 126. #469 | D67 | semidirect |
| 215. C8 | #11761627 | semidirect |