Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #424×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #424 | D67 |
| hypocenter | C67 | #3042 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11761617 | C2 | semidirect |
| 3. #16863972 | C2 | semidirect |
| 4. #16863870 | C2 | semidirect |
| 5. #16863612 | C2 | semidirect |
| 6. #16863602 | C2 | semidirect |
| 7. #16863406 | C2 | semidirect |
| 8. #16863393 | C2 | semidirect |
| 9. #424×C67 | C2 | semidirect |
| 18. #14524043 | C22 | semidirect |
| 19. #14524031 | C22 | semidirect |
| 26. #14523968 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 28. #14523965 | C22 | semidirect |
| 32. C4⋊C8×C67 | C22 | semidirect |
| 117. C67 | #3042 | semidirect |
| 124. #424 | D67 | semidirect |
| 146. C4⋊C8 | C2×D67 | semidirect |