Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16863876 | C2 | semidirect |
| 3. C2×#14523971 | C2 | semidirect |
| 4. #16863400 | C2 | semidirect |
| 5. #16863298 | C2 | semidirect |
| 6. #16863164 | C2 | semidirect |
| 7. #339×C67 | C2 | semidirect |
| 11. #14524071 | C4 | semidirect |
| 39. C2×D268 | C2×C4 | semidirect |
| 59. M16×C67 | C2×C4 | semidirect |
| 95. D268 | C22⋊C4 | semidirect |
| 100. Dic134 | C22⋊C4 | semidirect |
| 133. C67 | #1883 | semidirect |
| 140. #339 | D67 | semidirect |
| 185. M16 | C4×D67 | semidirect |