Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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×#14524040 | C2 | semidirect |
| 2. #16863772 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863591 | C2 | semidirect |
| 5. #16863529 | C2 | semidirect |
| 6. #16863449 | C2 | semidirect |
| 7. #532×C67 | C2 | semidirect |
| 11. C2×#11761613 | C22 | semidirect |
| 16. C4⋊(C67⋊C8) | C22 | semidirect |
| 17. #14523963 | C22 | semidirect |
| 19. C4×C67⋊C8 | C22 | semidirect |
| 21. C4⋊Q8×C67 | C22 | semidirect |
| 22. #127×C67 | C22 | semidirect |
| 27. C4×D4×C67 | C22 | semidirect |
| 74. C2×C4×C67 | D8 | semidirect |
| 113. C67 | #3205 | semidirect |
| 114. #532 | D67 | semidirect |
| 126. C4⋊Q8 | C2×D67 | semidirect |
| 131. #127 | C2×D67 | semidirect |
| 136. C4×D4 | C2×D67 | semidirect |
| 193. C2×C4 | #11761613 | semidirect |