Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #6432 | C4 | semidirect |
| 78. C4×C7 | #103 | semidirect |
| 125. C7 | #1981 | semidirect |
| 134. C4 | #6384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6432 | 2 |
| C4×C7×C4⋊C4 | 2 |
| C2×#6384 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| #1981 | 7 |