Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#11761617 | C2 | semidirect |
| 2. #16863967 | C2 | semidirect |
| 4. #16863642 | C2 | semidirect |
| 5. #16863625 | C2 | semidirect |
| 6. #16863434 | C2 | semidirect |
| 7. #16863406 | C2 | semidirect |
| 8. #16863402 | C2 | semidirect |
| 9. C2×#131×C67 | C2 | semidirect |
| 20. #14524022 | C22 | semidirect |
| 25. #14523977 | C22 | semidirect |
| 26. #14523975 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 32. C2×M16×C67 | C22 | semidirect |
| 34. C22×C8×C67 | C22 | semidirect |
| 67. C2×C8×C67 | D4 | semidirect |
| 121. C67 | #3057 | semidirect |
| 123. C2×#131 | D67 | semidirect |
| 139. C2×M16 | C2×D67 | semidirect |
| 141. C22×C8 | C2×D67 | semidirect |
| 179. C2×C8 | C22⋊D67 | semidirect |