Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. C7×#446 | C2 | semidirect |
| 4. Q8⋊(C7⋊C8) | C2 | semidirect |
| 6. #89274 | C2 | semidirect |
| 7. #89249 | C2 | semidirect |
| 42. #446 | D7 | semidirect |
| 68. C7⋊C8 | M16 | semidirect |
| 138. C7 | #1592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#446 | 2 |
| C4×#1143 | 2 |
| #89460 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| #89278 | 2 |
| #89274 | 2 |
| #89249 | 2 |
| #1592 | 7 |