Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864116 | C2 | semidirect |
| 2. #16863742 | C2 | semidirect |
| 3. #16863717 | C2 | semidirect |
| 4. #16863681 | C2 | semidirect |
| 5. #16863623 | C2 | semidirect |
| 6. #16863593 | C2 | semidirect |
| 7. #16863558 | C2 | semidirect |
| 8. C4×#11761618 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. #16863392 | C2 | semidirect |
| 128. C67 | #3304 | semidirect |