Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16864024 | C2 | semidirect |
| 3. #16863702 | C2 | semidirect |
| 4. #16863699 | C2 | semidirect |
| 5. #16863685 | C2 | semidirect |
| 6. #16863680 | C2 | semidirect |
| 7. C2×#14523974 | C2 | semidirect |
| 8. #16863424 | C2 | semidirect |
| 11. #428×C67 | C2 | semidirect |
| 42. #11761628 | Q8 | semidirect |
| 124. C67 | #3084 | semidirect |
| 131. #428 | D67 | semidirect |