Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #475×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #475 | D67 |
| hypocenter | C67 | #3298 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #475 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×D268 | C2 | semidirect |
| 3. #16863748 | C2 | semidirect |
| 4. #16863728 | C2 | semidirect |
| 5. #16863626 | C2 | semidirect |
| 6. #16863602 | C2 | semidirect |
| 7. #16863536 | C2 | semidirect |
| 8. C4×#11761615 | C2 | semidirect |
| 9. #16863461 | C2 | semidirect |
| 10. #103×D67 | C2 | semidirect |
| 11. #475×C67 | C2 | semidirect |
| 81. Q8×C67 | #41 | semidirect |
| 94. D268 | SD16 | semidirect |
| 129. C67 | #3298 | semidirect |
| 134. #475 | D67 | semidirect |
| 213. Q8 | #11761629 | semidirect |