Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. Q8×C7⋊C8 | C2 | semidirect |
| 4. Q8⋊(C7⋊C8) | C2 | semidirect |
| 6. #89253 | C2 | semidirect |
| 7. #89249 | C2 | semidirect |
| 51. C7×Q8 | M16 | semidirect |
| 120. Q8 | #1136 | semidirect |
| 138. C7 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×SD16 | 2 |
| Q8×C7⋊C8 | 2 |
| #89784 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| D4⋊(C7⋊C8) | 2 |
| #89253 | 2 |
| #89249 | 2 |
| #1588 | 7 |