Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #16864125 | C2 | semidirect |
| 3. #16863752 | C2 | semidirect |
| 5. #16863699 | C2 | semidirect |
| 6. #16863681 | C2 | semidirect |
| 7. #16863620 | C2 | semidirect |
| 9. C8×Dic134 | C2 | semidirect |
| 10. #16863481 | C2 | semidirect |
| 11. C4×Q16×C67 | C2 | semidirect |
| 118. C67 | #3365 | semidirect |
| 128. C4×Q16 | D67 | semidirect |