Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 61. C7×C8 | Q16 | semidirect |
| 128. C8 | #1144 | semidirect |
| 129. C7 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#446 | 2 |
| C4×#1144 | 2 |
| #89451 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| #89279 | 2 |
| #89274 | 2 |
| C8×C7⋊C8 | 2 |
| #1591 | 7 |