Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
150 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 62. C7×C8 | Q16 | semidirect |
| 126. C8 | #1144 | semidirect |
| 127. C7 | #1672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×Q8 | 2 |
| #89803 | 2 |
| #89793 | 2 |
| #89452 | 2 |
| #89281 | 2 |
| #89276 | 2 |
| #89252 | 2 |
| #1672 | 7 |