Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #419×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #419 | D67 |
| hypocenter | C67 | #2949 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #419 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863874 | C2 | semidirect |
| 4. #16863499 | C2 | semidirect |
| 5. #16863481 | C2 | semidirect |
| 6. #16863432 | C2 | semidirect |
| 8. #16863354 | C2 | semidirect |
| 9. #419×C67 | C2 | semidirect |
| 11. C2×#11761615 | C4 | semidirect |
| 16. Q8×Dic67 | C22 | semidirect |
| 23. #14523976 | C22 | semidirect |
| 24. #14523974 | C22 | semidirect |
| 26. #14523953 | C22 | semidirect |
| 27. C8×Dic67 | C22 | semidirect |
| 31. #103×C67 | C22 | semidirect |
| 38. #11761615 | C2×C4 | semidirect |
| 39. #11761615 | C2×C4 | semidirect |
| 40. C2×C67⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C67 | C2×C4 | semidirect |
| 104. C67 | #2949 | semidirect |
| 111. #419 | D67 | semidirect |
| 132. #103 | C2×D67 | semidirect |
| 139. C2×Q8 | C4×D67 | semidirect |