Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 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, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #424×C67 | C2 |
| hypercenter | #424 | D67 |
| hypocenter | C67 | #2929 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524051 | C2 | semidirect |
| 2. C22×C8×D67 | C2 | semidirect |
| 4. #16863466 | C2 | semidirect |
| 5. #16863461 | C2 | semidirect |
| 6. #16863362 | C2 | semidirect |
| 7. #16863359 | C2 | semidirect |
| 8. #16863352 | C2 | semidirect |
| 9. #424×C67 | C2 | semidirect |
| 14. C2×#11761611 | C22 | semidirect |
| 19. C2×C8×D67 | C22 | semidirect |
| 26. (C2×D67)⋊C8 | C22 | semidirect |
| 27. #14523954 | C22 | semidirect |
| 28. C4×C67⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C67 | C22 | semidirect |
| 48. C2×C67⋊C8 | D4 | semidirect |
| 101. C2×D67 | #131 | semidirect |
| 114. C67 | #2929 | semidirect |
| 120. #424 | D67 | semidirect |
| 142. C4⋊C8 | C2×D67 | semidirect |