Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #16863831 | C2 | semidirect |
| 2. C2×#14523984 | C2 | semidirect |
| 3. #16863666 | C2 | semidirect |
| 4. #16863209 | C2 | semidirect |
| 5. #16863203 | C2 | semidirect |
| 6. #16863180 | C2 | semidirect |
| 7. #576×C67 | C2 | semidirect |
| 9. C2×D536 | C22 | semidirect |
| 13. #14523983 | C22 | semidirect |
| 14. C2×C67⋊C16 | C22 | semidirect |
| 15. #14523979 | C22 | semidirect |
| 94. C67 | #2192 | semidirect |
| 95. #576 | D67 | semidirect |