Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #16864131 | C2 | semidirect |
| 2. #16863753 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863693 | C2 | semidirect |
| 5. #16863688 | C2 | semidirect |
| 6. #16863611 | C2 | semidirect |
| 8. Q8×C67⋊C8 | C2 | semidirect |
| 9. C4×#11761616 | C2 | semidirect |
| 10. C4×#11761613 | C2 | semidirect |
| 11. #554×C67 | C2 | semidirect |
| 123. C67 | #3361 | semidirect |
| 125. #554 | D67 | semidirect |