Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14523982 | C2 | semidirect |
| 3. #107×D67 | C2 | semidirect |
| 4. #16863200 | C2 | semidirect |
| 5. #16863198 | C2 | semidirect |
| 6. #16863196 | C2 | semidirect |
| 7. #358×C67 | C2 | semidirect |
| 10. #14524066 | C4 | semidirect |
| 31. D536 | C2×C4 | semidirect |
| 40. Q16×C67 | C2×C4 | semidirect |
| 82. C67 | #2139 | semidirect |
| 87. #358 | D67 | semidirect |
| 113. Q16 | C4×D67 | semidirect |