Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C2×#14524051 | C2 | semidirect |
| 3. #16863517 | C2 | direct (N × H) |
| 4. C2×#14523969 | C2 | semidirect |
| 5. C2×#14523953 | C2 | semidirect |
| 6. C2×#108×C67 | C2 | semidirect |
| 8. #14524065 | C4 | semidirect |
| 10. C2×Dic268 | C4 | semidirect |
| 11. C2×#11761617 | C4 | semidirect |
| 12. C2×D536 | C4 | semidirect |
| 14. #14524051 | C22 | semidirect |
| 19. #14523969 | C22 | semidirect |
| 20. #14523953 | C22 | semidirect |
| 23. #108×C67 | C22 | semidirect |
| 33. Dic268 | C2×C4 | semidirect |
| 34. #11761617 | C2×C4 | semidirect |
| 35. D536 | C2×C4 | semidirect |
| 88. C2×C67 | #444 | semidirect |
| 92. C67 | C2×#444 | semidirect |
| 96. C2×#108 | D67 | semidirect |
| 113. #108 | C2×D67 | semidirect |
| 181. C2 | #16863517 | direct (N × H) |