Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 3. #16863736 | C2 | direct (N × H) |
| 4. C2×#14523977 | C2 | semidirect |
| 5. C2×#14523974 | C2 | semidirect |
| 6. C2×#14523967 | C2 | semidirect |
| 8. C2×#103×C67 | C2 | semidirect |
| 21. #14523977 | C22 | semidirect |
| 22. #14523974 | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 28. #103×C67 | C22 | semidirect |
| 101. C2×C67 | #485 | semidirect |
| 107. C67 | C2×#485 | semidirect |
| 114. C2×#103 | D67 | semidirect |
| 134. #103 | C2×D67 | semidirect |
| 209. C2 | #16863736 | direct (N × H) |