Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#14523976 | C2 | semidirect |
| 5. #16863158 | C2 | semidirect |
| 6. #16863151 | C2 | semidirect |
| 7. #389×C67 | C2 | semidirect |
| 18. #14523963 | C4 | semidirect |
| 40. C2×C67⋊C8 | C2×C4 | semidirect |
| 53. C4⋊C4×C67 | C2×C4 | semidirect |
| 88. D268 | C4⋊C4 | semidirect |
| 124. C67 | #1862 | semidirect |
| 129. #389 | D67 | semidirect |
| 176. C4⋊C4 | C4×D67 | semidirect |