Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
908 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C2×#95×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C2×#95 | D67 |
| hypocenter | C67 | C2×#399 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊Dic67 | C2 | semidirect |
| 3. #16863333 | C2 | direct (N × H) |
| 4. C2×#95×C67 | C2 | semidirect |
| 8. C2×C4⋊Dic67 | C22 | semidirect |
| 12. #95×C67 | C22 | semidirect |
| 54. C2×C67 | #399 | semidirect |
| 60. C67 | C2×#399 | semidirect |
| 64. C2×#95 | D67 | semidirect |
| 72. #95 | C2×D67 | semidirect |
| 115. C2 | #16863333 | direct (N × H) |