Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C4×#120 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic67 | C2 | semidirect |
| 3. C2×(C22⋊D67)⋊C4 | C2 | semidirect |
| 4. #16863273 | C2 | semidirect |
| 5. #16863268 | C2 | semidirect |
| 6. C22⋊C4×Dic67 | C2 | semidirect |
| 7. #379×C67 | C2 | semidirect |
| 12. C22×C4×D67 | C22 | semidirect |
| 13. #14524012 | C4 | semidirect |
| 15. C2×Dic67⋊C4 | C22 | semidirect |
| 17. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic67 | C22 | semidirect |
| 19. C67⋊#95 | C22 | semidirect |
| 26. C2×C22⋊D67 | C2×C4 | semidirect |
| 31. C22×Dic67 | D4 | semidirect |
| 37. C22⋊Dic67 | C2×C4 | semidirect |
| 42. C24×C67 | C2×C4 | semidirect |
| 59. C22×D67 | C22×C4 | semidirect |
| 69. C2×Dic67 | C22×C4 | semidirect |
| 78. C22×C67 | C4×D4 | semidirect |
| 89. Dic67 | #120 | semidirect |
| 96. C67 | C4×#120 | semidirect |
| 102. #379 | D67 | semidirect |
| 122. C24 | C4×D67 | semidirect |
| 177. C22 | (C22⋊D67)⋊C4 | semidirect |