Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #433×C67 | C2 |
| hypercenter | #433 | D67 |
| hypocenter | C67 | #2978 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863475 | C2 | semidirect |
| 3. #16863473 | C2 | semidirect |
| 4. #16863469 | C2 | semidirect |
| 5. #16863466 | C2 | semidirect |
| 6. #16863457 | C2 | semidirect |
| 7. #16863361 | C2 | semidirect |
| 8. #16863358 | C2 | semidirect |
| 9. #433×C67 | C2 | semidirect |
| 14. C2×#11761611 | C22 | semidirect |
| 15. C2×C8×D67 | C22 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 26. (C2×D67)⋊C8 | C22 | semidirect |
| 27. (C2×D67)⋊C8 | C22 | semidirect |
| 28. #14523954 | C22 | semidirect |
| 29. C4×C67⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C67 | C22 | semidirect |
| 33. #97×C67 | C22 | semidirect |
| 34. C4×C8×C67 | C22 | semidirect |
| 115. C67 | #2978 | semidirect |
| 122. #433 | D67 | semidirect |
| 139. C4⋊C8 | C2×D67 | semidirect |
| 147. #97 | C2×D67 | semidirect |
| 149. C4×C8 | C2×D67 | semidirect |