Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #16864001 | C2 | semidirect |
| 2. #16863696 | C2 | semidirect |
| 3. #16863693 | C2 | semidirect |
| 4. #16863647 | C2 | semidirect |
| 5. #16863630 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863588 | C2 | semidirect |
| 8. #16863423 | C2 | semidirect |
| 9. #540×C67 | C2 | semidirect |
| 107. C67 | #3259 | semidirect |
| 109. #540 | D67 | semidirect |