Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #16864131 | C2 | semidirect |
| 2. #16863783 | C2 | semidirect |
| 3. #16863772 | C2 | semidirect |
| 4. #16863611 | C2 | semidirect |
| 5. #16863593 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863588 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 9. #16863506 | C2 | semidirect |
| 10. C4×#11761616 | C2 | semidirect |
| 11. #550×C67 | C2 | semidirect |
| 108. C67⋊C8 | #41 | semidirect |
| 135. C67 | #3399 | semidirect |
| 137. #550 | D67 | semidirect |