Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D268 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #405×C67 | C2 |
| socle | C2×C67 | C2×C4×D4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #2955 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524049 | C2 | semidirect |
| 3. #16863519 | C2 | semidirect |
| 4. #16863514 | C2 | semidirect |
| 5. #16863445 | C2 | semidirect |
| 6. #16863414 | C2 | semidirect |
| 7. #405×C67 | C2 | semidirect |
| 9. #14524076 | C4 | semidirect |
| 10. #14524071 | C4 | semidirect |
| 14. #14524049 | C22 | semidirect |
| 15. #14524049 | C22 | semidirect |
| 19. #14523979 | C22 | semidirect |
| 20. #14523971 | C22 | semidirect |
| 24. #97×C67 | C22 | semidirect |
| 25. C4×C8×C67 | C22 | semidirect |
| 90. C67 | #2955 | semidirect |
| 97. #405 | D67 | semidirect |
| 114. #97 | C2×D67 | semidirect |
| 115. C4×C8 | C2×D67 | semidirect |