Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16864103 | C2 | semidirect |
| 3. #16863794 | C2 | semidirect |
| 4. #16863727 | C2 | semidirect |
| 5. #16863715 | C2 | semidirect |
| 6. #16863687 | C2 | semidirect |
| 7. #16863682 | C2 | semidirect |
| 8. #16863625 | C2 | semidirect |
| 9. C4×#11761617 | C2 | semidirect |
| 10. C2×#14523975 | C2 | semidirect |
| 11. C8×D4×C67 | C2 | semidirect |
| 76. D4×C67 | SD16 | semidirect |
| 100. C8×C67 | #41 | semidirect |
| 124. C67 | #3335 | semidirect |
| 134. C8×D4 | D67 | semidirect |
| 207. D4 | #11761617 | semidirect |
| 224. C8 | #11761627 | semidirect |