Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×C16×D67 | C2 | semidirect |
| 3. #16863433 | C2 | semidirect |
| 4. #16863201 | C2 | semidirect |
| 5. #16863199 | C2 | semidirect |
| 6. #16863197 | C2 | semidirect |
| 7. #357×C67 | C2 | semidirect |
| 10. #14524062 | C4 | semidirect |
| 81. C67 | #2138 | semidirect |
| 88. #357 | D67 | semidirect |