Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
368 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14523974 | C2 | semidirect |
| 2. C2×#14523964 | C2 | semidirect |
| 3. C2×#14523964 | C2 | semidirect |
| 4. C2×C22⋊(C67⋊C8) | C2 | semidirect |
| 5. #16863256 | C2 | semidirect |
| 6. #16863158 | C2 | semidirect |
| 32. C2×C67⋊C8 | D4 | semidirect |
| 144. C67 | #2034 | semidirect |