Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #16864111 | C2 | semidirect |
| 2. #16863792 | C2 | semidirect |
| 3. #16863717 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863673 | C2 | semidirect |
| 7. #16863647 | C2 | semidirect |
| 8. C4×#11761613 | C2 | semidirect |
| 9. #16863474 | C2 | semidirect |
| 10. #16863436 | C2 | semidirect |
| 11. #547×C67 | C2 | semidirect |
| 101. C67⋊C8 | #41 | semidirect |
| 128. C67 | #3354 | semidirect |
| 130. #547 | D67 | semidirect |