Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #3162 |
| 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 |
|---|---|---|
| 3. #16863806 | C2 | semidirect |
| 4. #16863805 | C2 | semidirect |
| 5. #16863804 | C2 | semidirect |
| 6. #16863803 | C2 | semidirect |
| 7. #16863802 | C2 | semidirect |
| 11. #501×C67 | C2 | semidirect |
| 50. C8×D67 | Q8 | semidirect |
| 122. C67 | #3162 | semidirect |
| 130. #501 | D67 | semidirect |