Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #16864103 | C2 | semidirect |
| 2. #16864067 | C2 | semidirect |
| 3. #16863759 | C2 | semidirect |
| 4. #16863743 | C2 | semidirect |
| 5. #16863699 | C2 | semidirect |
| 6. #16863686 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863589 | C2 | semidirect |
| 9. #16863526 | C2 | semidirect |
| 10. #16863505 | C2 | semidirect |
| 11. C4×D8×C67 | C2 | semidirect |
| 80. D4×C67 | #41 | semidirect |
| 130. C67 | #3366 | semidirect |
| 141. C4×D8 | D67 | semidirect |
| 218. D4 | #11761628 | semidirect |