Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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 | #495×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #495 | D67 |
| hypocenter | C67 | #3280 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #495 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524066 | C2 | semidirect |
| 2. C2×D8×D67 | C2 | semidirect |
| 3. #16864039 | C2 | semidirect |
| 4. #16863634 | C2 | semidirect |
| 5. #16863629 | C2 | semidirect |
| 6. #16863608 | C2 | semidirect |
| 7. #16863545 | C2 | semidirect |
| 8. #16863540 | C2 | semidirect |
| 9. C4×D536 | C2 | semidirect |
| 10. C8×D268 | C2 | semidirect |
| 11. #495×C67 | C2 | semidirect |
| 12. C2×#11761629 | C22 | semidirect |
| 15. C2×#11761615 | C22 | semidirect |
| 20. C2×C8×D67 | C22 | semidirect |
| 24. #14524014 | C22 | semidirect |
| 27. C4×D268 | C22 | semidirect |
| 29. #14523977 | C22 | semidirect |
| 30. C4⋊(C67⋊C8) | C22 | semidirect |
| 31. #14523967 | C22 | semidirect |
| 32. #14523965 | C22 | semidirect |
| 33. #14523964 | C22 | semidirect |
| 35. (C2×D67)⋊C8 | C22 | semidirect |
| 36. C2×Q16×C67 | C22 | semidirect |
| 37. C2×SD16×C67 | C22 | semidirect |
| 39. #124×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 56. D536 | D4 | semidirect |
| 127. C2×D67 | #135 | semidirect |
| 144. C67 | #3280 | semidirect |
| 148. #495 | D67 | semidirect |
| 159. C2×Q16 | C2×D67 | semidirect |
| 161. C2×SD16 | C2×D67 | semidirect |
| 168. #124 | C2×D67 | semidirect |
| 184. C4×C8 | C2×D67 | semidirect |