Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 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. C22×#11761616 | C2 | semidirect |
| 2. C2×#14524051 | C2 | semidirect |
| 3. #16863972 | C2 | semidirect |
| 5. #16863641 | C2 | semidirect |
| 6. #16863624 | C2 | semidirect |
| 7. #16863432 | C2 | semidirect |
| 8. #16863406 | C2 | semidirect |
| 9. #418×C67 | C2 | semidirect |
| 16. C2×#11761611 | C22 | semidirect |
| 18. C2×C8×D67 | C22 | semidirect |
| 24. #14524023 | C22 | semidirect |
| 28. #14523976 | C22 | semidirect |
| 29. #14523974 | C22 | semidirect |
| 30. #14523968 | C22 | semidirect |
| 50. C2×C67⋊C8 | D4 | semidirect |
| 121. C67 | #3057 | semidirect |
| 130. #418 | D67 | semidirect |