Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. C7×#367 | C2 | semidirect |
| 5. #89299 | C2 | semidirect |
| 6. #89285 | C2 | semidirect |
| 7. #89284 | C2 | semidirect |
| 19. #6372 | C4 | semidirect |
| 34. C7×C16 | C2×C4 | semidirect |
| 35. C7⋊C16 | C2×C4 | semidirect |
| 40. #367 | D7 | semidirect |
| 93. C16 | C4×D7 | semidirect |
| 111. C7 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6372 | 2 |
| #89652 | 2 |
| D7×#107 | 2 |
| C7×#367 | 2 |
| #89299 | 2 |
| #89285 | 2 |
| #89284 | 2 |
| #2159 | 7 |