Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. #16863714 | C2 | direct (N × H) |
| 3. C2×#14523974 | C2 | semidirect |
| 4. C2×#14523963 | C2 | semidirect |
| 5. C2×C22⋊(C67⋊C8) | C2 | semidirect |
| 6. C22×C4⋊C4×C67 | C2 | semidirect |
| 14. #14523974 | C22 | semidirect |
| 15. #14523963 | C22 | semidirect |
| 16. C22⋊(C67⋊C8) | C22 | semidirect |
| 22. C2×C4⋊C4×C67 | C22 | semidirect |
| 90. C2×C67 | #481 | semidirect |
| 96. C67 | C2×#481 | semidirect |
| 98. C22×C4⋊C4 | D67 | semidirect |
| 114. C2×C4⋊C4 | C2×D67 | semidirect |
| 187. C2 | #16863714 | direct (N × H) |