Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D7 |
| commutator, socle | C22×C7 | C2×C42 |
| Fitting | C7×#431 | C2 |
| prime radical | C23×C7 | C42 |
| cosocle | C42×C7 | C23 |
| hypercenter | #431 | D7 |
| hypocenter | C7 | #1452 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #89250 | C2 | semidirect |
| 5. #89249 | C2 | semidirect |
| 100. C7 | #1452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#431 | 2 |
| #89697 | 2 |
| C2×C4×C7⋊C8 | 2 |
| #89250 | 2 |
| #89249 | 2 |
| #1452 | 7 |