Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #390×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #390 | D67 |
| hypocenter | C67 | #2328 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic67 | C2 | semidirect |
| 3. C2×#14524005 | C2 | semidirect |
| 4. #16863298 | C2 | semidirect |
| 5. #16863273 | C2 | semidirect |
| 6. #16863272 | C2 | semidirect |
| 7. #16863261 | C2 | semidirect |
| 8. #16863242 | C2 | semidirect |
| 9. #390×C67 | C2 | semidirect |
| 14. #14524039 | C4 | semidirect |
| 33. C2×D268 | C2×C4 | semidirect |
| 36. C2×C22⋊D67 | C2×C4 | semidirect |
| 49. C4×Dic67 | C2×C4 | semidirect |
| 50. C4×Dic67 | D4 | semidirect |
| 54. C2×D4×C67 | C2×C4 | semidirect |
| 124. C67 | #2328 | semidirect |
| 129. #390 | D67 | semidirect |
| 164. C2×D4 | C4×D67 | semidirect |