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. #16864116 | C2 | semidirect |
| 3. #16863747 | C2 | semidirect |
| 4. #16863738 | C2 | semidirect |
| 5. #16863677 | C2 | semidirect |
| 6. #16863637 | C2 | semidirect |
| 7. #16863607 | C2 | semidirect |
| 8. #16863560 | C2 | semidirect |
| 9. C4×#11761617 | C2 | semidirect |
| 10. #16863393 | C2 | semidirect |
| 11. C8×D4×C67 | C2 | semidirect |
| 126. C67 | #3302 | semidirect |
| 136. C8×D4 | D67 | semidirect |