Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524076 | C2 | semidirect |
| 3. C2×#14524073 | C2 | semidirect |
| 4. C2×#14524043 | C2 | semidirect |
| 5. #16863580 | C2 | direct (N × H) |
| 6. C2×#14523971 | C2 | semidirect |
| 7. C2×#14523961 | C2 | semidirect |
| 8. C2×#104×C67 | C2 | semidirect |
| 22. #14524076 | C22 | semidirect |
| 24. #14524073 | C22 | semidirect |
| 31. #14524043 | C22 | semidirect |
| 33. #14523971 | C22 | semidirect |
| 34. #14523961 | C22 | semidirect |
| 38. #104×C67 | C22 | semidirect |
| 167. C2×C67 | #456 | semidirect |
| 171. C67 | C2×#456 | semidirect |
| 178. C2×#104 | D67 | semidirect |
| 208. #104 | C2×D67 | semidirect |
| 339. C2 | #16863580 | direct (N × H) |