Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
160 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 18. C7×Q16 | C8 | semidirect |
| 63. Q16 | C7⋊C8 | semidirect |
| 88. C7 | #1579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×Q16 | 2 |
| Q8×C7⋊C8 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| #89252 | 2 |
| #89250 | 2 |
| #1579 | 7 |