Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
300 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 27. C4×Dic7 | C8 | semidirect |
| 70. C4×C7 | C4⋊C8 | semidirect |
| 75. Dic7 | C4⋊C8 | semidirect |
| 115. C7 | #1842 | semidirect |
| 124. C4 | Dic7⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊C8 | 2 |
| C2×Dic7⋊C8 | 2 |
| C42×Dic7 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| #1842 | 7 |