Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. C7×#107 | C4 | semidirect |
| 55. C7×C8 | C4⋊C4 | semidirect |
| 63. #107 | Dic7 | semidirect |
| 118. C8 | C4⋊Dic7 | semidirect |
| 119. C7 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#107 | 2 |
| C2×#6391 | 2 |
| C2×#6389 | 2 |
| #89757 | 2 |
| #89324 | 2 |
| #1943 | 7 |