Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11761617 | C2 | semidirect |
| 2. C2×#14524022 | C2 | semidirect |
| 4. #16863625 | C2 | direct (N × H) |
| 5. C2×#14523975 | C2 | semidirect |
| 6. C2×#14523968 | C2 | semidirect |
| 7. C2×#14523965 | C2 | semidirect |
| 8. C23×C8×C67 | C2 | semidirect |
| 13. C2×#11761617 | C22 | semidirect |
| 15. #14524022 | C22 | semidirect |
| 23. #14523975 | C22 | semidirect |
| 24. #14523968 | C22 | semidirect |
| 25. #14523965 | C22 | semidirect |
| 30. C22×C8×C67 | C22 | semidirect |
| 62. C2×C8×C67 | D4 | semidirect |
| 67. C23×C67 | SD16 | semidirect |
| 97. C8×C67 | C2×D4 | semidirect |
| 103. C22×C67 | C2×SD16 | semidirect |
| 118. C2×C67 | #465 | semidirect |
| 124. C67 | C2×#465 | semidirect |
| 126. C23×C8 | D67 | semidirect |
| 142. C22×C8 | C2×D67 | semidirect |
| 179. C2×C8 | C22⋊D67 | semidirect |
| 195. C23 | #11761617 | semidirect |
| 221. C8 | C2×C22⋊D67 | semidirect |
| 231. C22 | C2×#11761617 | semidirect |
| 243. C2 | #16863625 | direct (N × H) |