Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #16863223 | C2 | semidirect |
| 3. #16863221 | C2 | semidirect |
| 4. #16863196 | C2 | semidirect |
| 5. #16863196 | C2 | semidirect |
| 6. C22⋊(C67⋊C16) | C2 | semidirect |
| 7. #427×C67 | C2 | semidirect |
| 70. C67 | #2234 | semidirect |
| 72. #427 | D67 | semidirect |