Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#14524069 | C2 | semidirect |
| 2. C2×#14524049 | C2 | semidirect |
| 3. #16863663 | C2 | direct (N × H) |
| 4. C2×#14523979 | C2 | semidirect |
| 5. C2×#14523960 | C2 | semidirect |
| 6. C22×D8×C67 | C2 | semidirect |
| 9. #14524069 | C22 | semidirect |
| 13. #14524049 | C22 | semidirect |
| 18. #14523979 | C22 | semidirect |
| 19. #14523960 | C22 | semidirect |
| 24. C2×D8×C67 | C22 | semidirect |
| 105. C2×C67 | #472 | semidirect |
| 109. C67 | C2×#472 | semidirect |
| 111. C22×D8 | D67 | semidirect |
| 125. C2×D8 | C2×D67 | semidirect |
| 215. C2 | #16863663 | direct (N × H) |