Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #16864111 | C2 | semidirect |
| 2. #16863746 | C2 | semidirect |
| 3. #16863734 | C2 | semidirect |
| 4. #16863686 | C2 | semidirect |
| 5. #16863627 | C2 | semidirect |
| 6. #16863598 | C2 | semidirect |
| 7. #16863541 | C2 | semidirect |
| 8. C4×#11761613 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. #16863392 | C2 | semidirect |
| 11. #547×C67 | C2 | semidirect |
| 131. C67 | #3303 | semidirect |
| 133. #547 | D67 | semidirect |