Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C22×#11761611 | C2 | semidirect |
| 3. C2×C4⋊C4×D67 | C2 | semidirect |
| 4. #16863396 | C2 | direct (N × H) |
| 5. C2×#14523967 | C2 | semidirect |
| 6. C2×#14523965 | C2 | semidirect |
| 7. C2×#14523963 | C2 | semidirect |
| 8. C2×#103×C67 | C2 | semidirect |
| 11. C2×#11761629 | C4 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 24. C4⋊C4×D67 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 26. #14523965 | C22 | semidirect |
| 27. #14523963 | C22 | semidirect |
| 31. #103×C67 | C22 | semidirect |
| 36. #11761629 | C2×C4 | semidirect |
| 41. C2×D268 | C2×C4 | semidirect |
| 61. C2×Q8×C67 | C2×C4 | semidirect |
| 81. Q8×C67 | C22×C4 | semidirect |
| 97. D268 | C22×C4 | semidirect |
| 124. C2×C67 | #417 | semidirect |
| 131. C67 | C2×#417 | semidirect |
| 137. C2×#103 | D67 | semidirect |
| 160. #103 | C2×D67 | semidirect |
| 170. C2×Q8 | C4×D67 | semidirect |
| 212. Q8 | C2×C4×D67 | semidirect |
| 257. C2 | #16863396 | direct (N × H) |