Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #500×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #500 | D67 |
| hypocenter | C67 | #3353 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864120 | C2 | semidirect |
| 3. #16863733 | C2 | semidirect |
| 4. #16863723 | C2 | semidirect |
| 5. #16863678 | C2 | semidirect |
| 6. #16863673 | C2 | semidirect |
| 7. #16863643 | C2 | semidirect |
| 8. C4×#11761617 | C2 | semidirect |
| 9. #16863475 | C2 | semidirect |
| 10. #16863437 | C2 | semidirect |
| 11. #500×C67 | C2 | semidirect |
| 98. C8×C67 | #41 | semidirect |
| 123. C67 | #3353 | semidirect |
| 126. #500 | D67 | semidirect |
| 222. C8 | #11761629 | semidirect |