Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14523971 | C2 | semidirect |
| 3. C2×#14523970 | C2 | semidirect |
| 4. C2×#14523969 | C2 | semidirect |
| 5. M16×Dic67 | C2 | semidirect |
| 6. C4×Dic67⋊C4 | C2 | semidirect |
| 7. C2×#104×C67 | C2 | semidirect |
| 10. #14524041 | C4 | semidirect |
| 11. #14524039 | C4 | semidirect |
| 12. #14524032 | C4 | semidirect |
| 13. #14524030 | C4 | semidirect |
| 45. #11761612 | D4 | semidirect |
| 71. M16×C67 | D4 | semidirect |
| 140. Dic67 | #104 | semidirect |
| 149. C67 | #1980 | semidirect |
| 154. C2×#104 | D67 | semidirect |
| 206. M16 | C22⋊D67 | semidirect |