Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16864103 | C2 | semidirect |
| 2. #16863792 | C2 | semidirect |
| 3. #16863726 | C2 | semidirect |
| 4. #16863712 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863678 | C2 | semidirect |
| 7. #16863623 | C2 | semidirect |
| 8. C4×#11761616 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. C2×#14523974 | C2 | semidirect |
| 80. D4×C67 | SD16 | semidirect |
| 100. C67⋊C8 | #41 | semidirect |
| 124. C67 | #3335 | semidirect |
| 207. D4 | #11761616 | semidirect |