Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×C22⋊D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #578×C67 | C2 |
| socle | C2×C67 | D42 |
| hypercenter | #578 | D67 |
| hypocenter | C67 | #3293 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #578 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864211 | C2 | semidirect |
| 2. #16864210 | C2 | semidirect |
| 3. #16863774 | C2 | semidirect |
| 4. #16863671 | C2 | semidirect |
| 5. #16863669 | C2 | semidirect |
| 6. #16863668 | C2 | semidirect |
| 7. #16863579 | C2 | semidirect |
| 8. #16863577 | C2 | semidirect |
| 9. #16863513 | C2 | semidirect |
| 10. #16863511 | C2 | semidirect |
| 11. #578×C67 | C2 | semidirect |
| 147. C67 | #3293 | semidirect |
| 150. #578 | D67 | semidirect |