Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16864131 | C2 | semidirect |
| 2. #16863778 | C2 | semidirect |
| 3. #16863770 | C2 | semidirect |
| 4. #16863618 | C2 | semidirect |
| 5. #16863608 | C2 | semidirect |
| 6. #16863603 | C2 | semidirect |
| 8. Q8×C67⋊C8 | C2 | semidirect |
| 9. C4×#11761615 | C2 | semidirect |
| 10. C4×#11761616 | C2 | semidirect |
| 11. #556×C67 | C2 | semidirect |
| 126. C67 | #3394 | semidirect |
| 128. #556 | D67 | semidirect |