Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #501×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #501 | D67 |
| hypocenter | C67 | #3234 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #501 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #125×D67 | C2 | semidirect |
| 3. #16863802 | C2 | semidirect |
| 4. #16863762 | C2 | semidirect |
| 5. #16863761 | C2 | semidirect |
| 6. #16863716 | C2 | semidirect |
| 7. #16863711 | C2 | semidirect |
| 8. #16863699 | C2 | semidirect |
| 9. #16863695 | C2 | semidirect |
| 10. #16863451 | C2 | semidirect |
| 11. #501×C67 | C2 | semidirect |
| 129. C67 | #3234 | semidirect |
| 133. #501 | D67 | semidirect |