Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#14524065 | C2 | semidirect |
| 2. C2×#14524063 | C2 | semidirect |
| 3. #16863942 | C2 | semidirect |
| 4. #16863789 | C2 | semidirect |
| 5. #16863787 | C2 | semidirect |
| 6. #16863784 | C2 | semidirect |
| 7. #16863782 | C2 | semidirect |
| 8. C2×#14523953 | C2 | semidirect |
| 9. C2×#135×C67 | C2 | semidirect |
| 51. C2×C67⋊C8 | D4 | semidirect |
| 68. C2×C8×C67 | D4 | semidirect |
| 117. C67 | #3150 | semidirect |
| 120. C2×#135 | D67 | semidirect |
| 180. C2×C8 | C22⋊D67 | semidirect |