Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting | C7×#432 | C2 |
| prime radical | C23×C7 | C22×C4 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | #432 | D7 |
| hypocenter | C7 | #2987 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #89600 | C2 | semidirect |
| 6. #89473 | C2 | semidirect |
| 136. C7 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90161 | 2 |
| C7×#432 | 2 |
| #89698 | 2 |
| #89600 | 2 |
| #89492 | 2 |
| #89473 | 2 |
| #2987 | 7 |