Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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. D4×Dic134 | C2 | semidirect |
| 2. #16863748 | C2 | semidirect |
| 3. #16863726 | C2 | semidirect |
| 4. #16863678 | C2 | semidirect |
| 5. #16863623 | C2 | semidirect |
| 6. #16863601 | C2 | semidirect |
| 7. #16863534 | C2 | semidirect |
| 8. C4×#11761616 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. C2×#14523966 | C2 | semidirect |
| 83. D4×C67 | SD16 | semidirect |
| 102. Dic134 | #41 | semidirect |
| 129. C67 | #3298 | semidirect |
| 217. D4 | #11761616 | semidirect |