Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting | #123×C167 | C2 |
| prime radical | #19128800 | C2 |
| hypercenter | #123 | D167 |
| hypocenter | C167 | #551 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128825 | C2 | semidirect |
| 2. #19128819 | C2 | semidirect |
| 3. #19128814 | C2 | semidirect |
| 4. #19128810 | C2 | semidirect |
| 6. C4×C22⋊D167 | C2 | semidirect |
| 7. #19128790 | C2 | semidirect |
| 8. C22⋊C4×D167 | C2 | semidirect |
| 9. #123×C167 | C2 | semidirect |
| 11. C2×Dic334 | C22 | semidirect |
| 15. C4⋊Dic167 | C22 | semidirect |
| 16. Dic167⋊C4 | C22 | semidirect |
| 17. Dic167⋊C4 | C22 | semidirect |
| 20. C22⋊Dic167 | C22 | semidirect |
| 24. C4×Dic167 | C22 | semidirect |
| 25. C4×Dic167 | C22 | semidirect |
| 27. C22×C4×C167 | C22 | semidirect |
| 28. C4⋊C4×C167 | C22 | semidirect |
| 30. C22⋊C4×C167 | C22 | semidirect |
| 68. C167 | #551 | semidirect |
| 73. #123 | D167 | semidirect |
| 85. C22×C4 | C2×D167 | semidirect |
| 89. C4⋊C4 | C2×D167 | semidirect |
| 97. C22⋊C4 | C2×D167 | semidirect |