Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| hypercenter | #123 | D167 |
| hypocenter | C167 | #547 |
| 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. C2×#14581950 | C2 | semidirect |
| 2. C2×#14581949 | C2 | semidirect |
| 3. #19128831 | C2 | semidirect |
| 4. #19128817 | C2 | semidirect |
| 5. #19128816 | C2 | semidirect |
| 6. #19128814 | C2 | semidirect |
| 7. #19128810 | C2 | semidirect |
| 8. #19128809 | C2 | semidirect |
| 9. #19128805 | C2 | semidirect |
| 10. #19128804 | C2 | semidirect |
| 11. (C22⋊D167)⋊C4 | C2 | semidirect |
| 12. (C22⋊D167)⋊C4 | C2 | semidirect |
| 13. C2×Dic167⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D167 | C2 | semidirect |
| 15. #123×C167 | C2 | semidirect |
| 61. C22⋊D167 | D4 | semidirect |
| 107. Dic167 | #41 | semidirect |
| 115. C167 | #547 | semidirect |
| 123. #123 | D167 | semidirect |