Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #427×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #427 | D67 |
| hypocenter | C67 | #2912 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16863439 | C2 | semidirect |
| 4. #16863437 | C2 | semidirect |
| 5. #16863431 | C2 | semidirect |
| 6. C2×#14523975 | C2 | semidirect |
| 7. #106×D67 | C2 | semidirect |
| 8. #427×C67 | C2 | semidirect |
| 10. #14524049 | C4 | semidirect |
| 37. #11761612 | C2×C4 | semidirect |
| 38. #11761611 | C2×C4 | semidirect |
| 40. C8×D67 | C2×C4 | semidirect |
| 47. C2×C8×C67 | C2×C4 | semidirect |
| 91. C67 | #2912 | semidirect |
| 97. #427 | D67 | semidirect |
| 133. C2×C8 | C4×D67 | semidirect |