Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C7 |
| prime radical | C23×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #2089 | C7 | direct (N × H) |
| 98. C7 | #2089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#428 | 2 |
| C2×C7×#107 | 2 |
| C7×#424 | 2 |
| C7×#343 | 2 |
| C7×#341 | 2 |
| #2089 | 7 |