Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C167 | C2 |
| hypercenter | C4×D4 | D167 |
| hypocenter | C167 | #553 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128827 | C2 | semidirect |
| 2. #19128824 | C2 | semidirect |
| 3. #19128814 | C2 | semidirect |
| 4. #19128806 | C2 | semidirect |
| 5. #19128806 | C2 | semidirect |
| 6. #19128804 | C2 | semidirect |
| 7. C4×D668 | C2 | semidirect |
| 8. (C22⋊D167)⋊C4 | C2 | semidirect |
| 9. #19128791 | C2 | semidirect |
| 10. C2×C4⋊Dic167 | C2 | semidirect |
| 11. C4×D4×C167 | C2 | semidirect |
| 78. C167 | #553 | semidirect |
| 88. C4×D4 | D167 | semidirect |