Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C4×#11761612 | C2 | semidirect |
| 4. #16863164 | C2 | semidirect |
| 5. C4×M16×C67 | C2 | semidirect |
| 15. #14523959 | C4 | direct (N × H) |
| 32. #11761612 | C2×C4 | semidirect |
| 42. M16×C67 | C2×C4 | semidirect |
| 85. C4×C67 | #100 | semidirect |
| 96. C67 | C4×#100 | semidirect |
| 100. C4×M16 | D67 | semidirect |
| 133. M16 | C4×D67 | semidirect |
| 182. C4 | #14523959 | direct (N × H) |