Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#11761616 | C2 | semidirect |
| 4. C2×#14524008 | C2 | semidirect |
| 5. #16863595 | C2 | direct (N × H) |
| 6. C2×Dic67⋊C8 | C2 | semidirect |
| 7. C2×#14523963 | C2 | semidirect |
| 8. C2×#102×C67 | C2 | semidirect |
| 14. C2×#11761617 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 21. #14524008 | C22 | semidirect |
| 25. Dic67⋊C8 | C22 | semidirect |
| 26. #14523963 | C22 | semidirect |
| 30. #102×C67 | C22 | semidirect |
| 34. C2×Dic134 | D4 | semidirect |
| 89. C2×Dic67 | SD16 | semidirect |
| 97. Dic134 | C2×D4 | semidirect |
| 118. Dic67 | C2×SD16 | semidirect |
| 120. C2×C67 | #460 | semidirect |
| 126. C67 | C2×#460 | semidirect |
| 134. C2×#102 | D67 | semidirect |
| 156. #102 | C2×D67 | semidirect |
| 247. C2 | #16863595 | direct (N × H) |