Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #486×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #486 | D67 |
| hypocenter | C67 | #3295 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864107 | C2 | semidirect |
| 3. #16863713 | C2 | semidirect |
| 4. #16863683 | C2 | semidirect |
| 5. #16863624 | C2 | semidirect |
| 6. #16863593 | C2 | semidirect |
| 7. #16863548 | C2 | semidirect |
| 8. C4×#11761617 | C2 | semidirect |
| 9. C8×D268 | C2 | semidirect |
| 10. #102×D67 | C2 | semidirect |
| 11. #486×C67 | C2 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 16. C2×C8×D67 | C22 | semidirect |
| 18. #14524023 | C22 | semidirect |
| 23. C4×Dic134 | C22 | semidirect |
| 27. C4⋊C4×D67 | C22 | semidirect |
| 28. #14523975 | C22 | semidirect |
| 29. #14523974 | C22 | semidirect |
| 30. C4⋊(C67⋊C8) | C22 | semidirect |
| 31. #14523968 | C22 | semidirect |
| 33. #14523964 | C22 | semidirect |
| 35. (C2×D67)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C67 | C22 | semidirect |
| 38. #102×C67 | C22 | semidirect |
| 39. #102×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 99. D268 | SD16 | semidirect |
| 137. C67 | #3295 | semidirect |
| 140. #486 | D67 | semidirect |
| 154. C4⋊Q8 | C2×D67 | semidirect |
| 174. #102 | C2×D67 | semidirect |
| 175. #102 | C2×D67 | semidirect |
| 177. C4×C8 | C2×D67 | semidirect |