Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864067 | C2 | semidirect |
| 3. #16863782 | C2 | semidirect |
| 4. #16863773 | C2 | semidirect |
| 5. #16863614 | C2 | semidirect |
| 6. #16863596 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863590 | C2 | semidirect |
| 9. #16863526 | C2 | semidirect |
| 10. #16863507 | C2 | semidirect |
| 11. C4×SD16×C67 | C2 | semidirect |
| 107. C8×C67 | #41 | semidirect |
| 135. C67 | #3399 | semidirect |
| 146. C4×SD16 | D67 | semidirect |
| 243. C8 | #11761628 | semidirect |