Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 7. C7×C4⋊Q8 | C4 | semidirect |
| 55. C4⋊Q8 | Dic7 | semidirect |
| 68. C4×C7 | #103 | semidirect |
| 109. C7 | #1956 | semidirect |
| 117. C4 | #6409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊Q8 | 2 |
| C2×#6409 | 2 |
| #89707 | 2 |
| C2×C4×C7⋊C8 | 2 |
| #1956 | 7 |