Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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, socle | C23×C67 | C24 |
| Fitting | C2×C22⋊Q8×C67 | C2 |
| hypercenter | C2×C22⋊Q8 | D67 |
| hypocenter | C67 | #2561 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863322 | C2 | semidirect |
| 3. #16863307 | C2 | semidirect |
| 4. #16863286 | C2 | semidirect |
| 5. #16863257 | C2 | semidirect |
| 7. C4×C22⋊Dic67 | C2 | semidirect |
| 8. C2×C22⋊Q8×C67 | C2 | semidirect |
| 17. C2×C4×Dic67 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 19. C67⋊#95 | C22 | semidirect |
| 20. C67⋊#95 | C22 | semidirect |
| 21. C22×Q8×C67 | C22 | semidirect |
| 24. C2×C4⋊C4×C67 | C22 | semidirect |
| 25. C2×C4⋊C4×C67 | C22 | semidirect |
| 111. C67 | #2561 | semidirect |
| 112. C2×C22⋊Q8 | D67 | semidirect |
| 121. C22×Q8 | C2×D67 | semidirect |
| 125. C2×C4⋊C4 | C2×D67 | semidirect |
| 126. C2×C4⋊C4 | C2×D67 | semidirect |