Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
430 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 430 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. #16864068 | C2 | semidirect |
| 2. #16864051 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863716 | C2 | semidirect |
| 5. #16863681 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863540 | C2 | semidirect |
| 9. #16863475 | C2 | semidirect |
| 10. #16863396 | C2 | semidirect |
| 11. C4×SD16×C67 | C2 | semidirect |
| 81. Q8×C67 | #41 | semidirect |
| 135. C67 | #3332 | semidirect |
| 144. C4×SD16 | D67 | semidirect |
| 217. Q8 | #11761628 | semidirect |