Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #16863693 | C2 | direct (N × H) |
| 3. C2×#14523976 | C2 | semidirect |
| 4. C2×#14523974 | C2 | semidirect |
| 5. C2×C4⋊(C67⋊C8) | C2 | semidirect |
| 8. C2×#125×C67 | C2 | semidirect |
| 17. #14523976 | C22 | semidirect |
| 18. #14523974 | C22 | semidirect |
| 19. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #125×C67 | C22 | semidirect |
| 98. C2×C67 | #478 | semidirect |
| 104. C67 | C2×#478 | semidirect |
| 105. C2×#125 | D67 | semidirect |
| 118. #125 | C2×D67 | semidirect |
| 203. C2 | #16863693 | direct (N × H) |