Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #430×C67 | C2 |
| socle | C2×C67 | C2×C4×D4 |
| hypercenter | #430 | D67 |
| hypocenter | C67 | #2956 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #430 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16864162 | C2 | semidirect |
| 3. #16863517 | C2 | semidirect |
| 4. #16863512 | C2 | semidirect |
| 5. C2×#14523969 | C2 | semidirect |
| 6. M16×Dic67 | C2 | semidirect |
| 7. #430×C67 | C2 | semidirect |
| 9. #14524076 | C4 | semidirect |
| 10. #14524071 | C4 | semidirect |
| 12. #14524051 | C22 | semidirect |
| 17. #14523969 | C22 | semidirect |
| 18. #14523969 | C22 | semidirect |
| 19. #14523953 | C22 | semidirect |
| 20. C8×Dic67 | C22 | semidirect |
| 23. #108×C67 | C22 | semidirect |
| 33. Dic268 | C2×C4 | semidirect |
| 34. #11761617 | C2×C4 | semidirect |
| 35. D536 | C2×C4 | semidirect |
| 86. C67 | #2956 | semidirect |
| 91. #430 | D67 | semidirect |
| 105. #108 | C2×D67 | semidirect |