Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | #379×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #379 | D67 |
| hypocenter | C67 | #2375 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863296 | C2 | semidirect |
| 3. #16863290 | C2 | semidirect |
| 4. #16863284 | C2 | semidirect |
| 5. #16863272 | C2 | semidirect |
| 6. #16863252 | C2 | semidirect |
| 7. #379×C67 | C2 | semidirect |
| 9. C22×C4×D67 | C22 | semidirect |
| 10. #14524012 | C4 | semidirect |
| 11. C2×Dic67⋊C4 | C22 | semidirect |
| 15. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic67 | C22 | semidirect |
| 17. C67⋊#95 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 33. C22⋊Dic67 | C2×C4 | semidirect |
| 38. C24×C67 | C2×C4 | semidirect |
| 96. C67 | #2375 | semidirect |
| 103. #379 | D67 | semidirect |
| 121. C24 | C4×D67 | semidirect |