Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C23×C67⋊C8 | C2 | semidirect |
| 3. C2×#14524022 | C2 | semidirect |
| 4. #16863623 | C2 | direct (N × H) |
| 5. C2×#14523974 | C2 | semidirect |
| 6. C2×#14523966 | C2 | semidirect |
| 7. C2×#14523964 | C2 | semidirect |
| 11. C2×#11761616 | C22 | semidirect |
| 15. C22×C67⋊C8 | C22 | semidirect |
| 17. #14524022 | C22 | semidirect |
| 21. #14523974 | C22 | semidirect |
| 22. #14523966 | C22 | semidirect |
| 23. #14523964 | C22 | semidirect |
| 40. C2×C67⋊C8 | D4 | semidirect |
| 71. C23×C67 | SD16 | semidirect |
| 97. C67⋊C8 | C2×D4 | semidirect |
| 107. C22×C67 | C2×SD16 | semidirect |
| 119. C2×C67 | #465 | semidirect |
| 124. C67 | C2×#465 | semidirect |
| 195. C23 | #11761616 | semidirect |
| 231. C22 | C2×#11761616 | semidirect |
| 243. C2 | #16863623 | direct (N × H) |