Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #3079 |
| 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. C4⋊Q8×D67 | C2 | semidirect |
| 3. #16863689 | C2 | semidirect |
| 4. #16863685 | C2 | semidirect |
| 5. #16863681 | C2 | semidirect |
| 6. #16863677 | C2 | semidirect |
| 7. #16863673 | C2 | semidirect |
| 8. #16863435 | C2 | semidirect |
| 9. #16863418 | C2 | semidirect |
| 11. #475×C67 | C2 | semidirect |
| 44. #11761629 | Q8 | semidirect |
| 86. Q8×C67 | C2×Q8 | semidirect |
| 100. D268 | C2×Q8 | semidirect |
| 138. C67 | #3079 | semidirect |
| 144. #475 | D67 | semidirect |
| 226. Q8 | Q8×D67 | semidirect |