Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | #379×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #379 | D67 |
| hypocenter | C67 | C2×#379 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×D67 | C2 | semidirect |
| 3. #16863252 | C2 | semidirect |
| 4. #16863251 | C2 | semidirect |
| 5. #379×C67 | C2 | semidirect |
| 7. C24×D67 | C4 | semidirect |
| 10. C22×C4×D67 | C22 | semidirect |
| 11. C2×C22⋊Dic67 | C22 | semidirect |
| 12. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 15. C2×C22⋊C4×C67 | C22 | semidirect |
| 22. C23×D67 | C2×C4 | semidirect |
| 26. C22×Dic67 | C23 | semidirect |
| 31. C24×C67 | C2×C4 | semidirect |
| 33. C22×C4×C67 | C23 | semidirect |
| 48. C22×D67 | C22⋊C4 | semidirect |
| 59. C22×C67 | C2×C22⋊C4 | semidirect |
| 67. C2×D67 | C2×C22⋊C4 | semidirect |
| 75. D67 | #379 | direct (N × H) |
| 77. C67 | C2×#379 | semidirect |
| 82. #379 | D67 | direct (N × H) |
| 92. C2×C22⋊C4 | C2×D67 | semidirect |
| 104. C24 | C4×D67 | semidirect |
| 108. C22×C4 | C22×D67 | semidirect |
| 143. C22 | C22⋊C4×D67 | semidirect |