Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 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, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | C24×C4×C67 | C2 |
| hypercenter | C24×C4 | D67 |
| hypocenter | C67 | #2849 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524026 | C2 | semidirect |
| 3. #16863275 | C2 | semidirect |
| 4. #16863269 | C2 | semidirect |
| 5. #16863259 | C2 | semidirect |
| 6. #16863252 | C2 | semidirect |
| 7. C24×C4×C67 | C2 | semidirect |
| 12. C2×Dic67⋊C4 | C22 | semidirect |
| 17. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 48. C22×C4×C67 | D4 | semidirect |
| 84. C22×C67 | #123 | semidirect |
| 102. C67 | #2849 | semidirect |
| 103. C24×C4 | D67 | semidirect |
| 144. C22×C4 | C22⋊D67 | semidirect |
| 189. C22 | #14524026 | semidirect |