Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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 | C22×D167 |
| commutator, socle, cosocle | C23×C167 | C23 |
| Fitting | #95×C167 | C2 |
| prime radical | C23×D167 | C22 |
| hypercenter | #95 | D167 |
| hypocenter | C167 | #397 |
| LCS | G ▷ C23×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊Dic167 | C2 | semidirect |
| 4. C167⋊#95 | C2 | semidirect |
| 5. #95×C167 | C2 | semidirect |
| 50. C167 | #397 | semidirect |
| 56. #95 | D167 | semidirect |