Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C7×#107 | C4 | semidirect |
| 59. C7×C8 | C4⋊C4 | semidirect |
| 68. #107 | Dic7 | semidirect |
| 131. C8 | C4⋊Dic7 | semidirect |
| 132. C7 | #1942 | 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×#6392 | 2 |
| C2×C8×Dic7 | 2 |
| #89757 | 2 |
| #89324 | 2 |
| #1942 | 7 |