Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14524049 | C2 | semidirect |
| 2. #16863970 | C2 | semidirect |
| 4. #16863639 | C2 | semidirect |
| 5. #16863622 | C2 | semidirect |
| 6. #16863434 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863401 | C2 | semidirect |
| 9. C22×SD16×C67 | C2 | semidirect |
| 13. C2×#11761611 | C22 | semidirect |
| 14. C2×C8×D67 | C22 | semidirect |
| 20. #14524019 | C22 | semidirect |
| 25. #14523977 | C22 | semidirect |
| 26. #14523975 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 68. C2×C8×C67 | D4 | semidirect |
| 121. C67 | #3057 | semidirect |
| 122. C22×SD16 | D67 | semidirect |
| 180. C2×C8 | C22⋊D67 | semidirect |