Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524073 | C2 | semidirect |
| 2. C2×#14524068 | C2 | semidirect |
| 3. C2×#14524031 | C2 | semidirect |
| 4. #16863788 | C2 | semidirect |
| 5. #16863783 | C2 | semidirect |
| 6. #16863778 | C2 | semidirect |
| 7. C4×#11761612 | C2 | semidirect |
| 8. #532×C67 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761616 | C22 | semidirect |
| 22. #14523954 | C22 | semidirect |
| 23. C4×C67⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C67 | C22 | semidirect |
| 26. #127×C67 | C22 | semidirect |
| 27. #124×C67 | C22 | semidirect |
| 43. #11761612 | D4 | semidirect |
| 107. C67 | #3153 | semidirect |
| 110. #532 | D67 | semidirect |
| 126. C4⋊Q8 | C2×D67 | semidirect |
| 127. #127 | C2×D67 | semidirect |
| 131. #124 | C2×D67 | semidirect |