Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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. C2×#14524076 | C2 | semidirect |
| 3. C22×#11761617 | C2 | semidirect |
| 4. C2×#14524049 | C2 | semidirect |
| 5. #16863660 | C2 | direct (N × H) |
| 6. C2×#14523961 | C2 | semidirect |
| 7. C2×#14523959 | C2 | semidirect |
| 8. C2×#108×C67 | C2 | semidirect |
| 13. #14524076 | C22 | semidirect |
| 22. C2×#11761617 | C22 | semidirect |
| 25. #14524049 | C22 | semidirect |
| 29. #14523961 | C22 | semidirect |
| 30. #14523959 | C22 | semidirect |
| 34. #108×C67 | C22 | semidirect |
| 134. C2×C67 | #471 | semidirect |
| 139. C67 | C2×#471 | semidirect |
| 145. C2×#108 | D67 | semidirect |
| 171. #108 | C2×D67 | semidirect |
| 275. C2 | #16863660 | direct (N × H) |