Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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. #16863781 | C2 | semidirect |
| 3. #16863513 | C2 | semidirect |
| 4. #16863216 | C2 | semidirect |
| 5. #16863212 | C2 | semidirect |
| 6. #16863210 | C2 | semidirect |
| 7. #510×C67 | C2 | semidirect |
| 75. C67 | #2212 | semidirect |
| 76. #510 | D67 | semidirect |