Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C2×#125×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C2×#125 | D67 |
| hypocenter | C67 | C2×#541 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864009 | C2 | direct (N × H) |
| 2. C2×#14524043 | C2 | semidirect |
| 4. C2×#14524034 | C2 | semidirect |
| 6. C2×#14524008 | C2 | semidirect |
| 8. C2×#125×C67 | C2 | semidirect |
| 11. #14524043 | C22 | semidirect |
| 13. #14524034 | C22 | semidirect |
| 15. #14524008 | C22 | semidirect |
| 25. #125×C67 | C22 | semidirect |
| 81. C2×C67 | #541 | semidirect |
| 86. C67 | C2×#541 | semidirect |
| 91. C2×#125 | D67 | semidirect |
| 100. #125 | C2×D67 | semidirect |
| 168. C2 | #16864009 | direct (N × H) |