Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. C7×#427 | C2 | semidirect |
| 4. C2×#6391 | C2 | semidirect |
| 5. #89767 | C2 | semidirect |
| 6. #89653 | C2 | semidirect |
| 7. #89632 | C2 | semidirect |
| 8. D7×#106 | C2 | semidirect |
| 14. #6464 | C4 | semidirect |
| 39. C2×C7×C8 | C2×C4 | semidirect |
| 51. #1136 | C2×C4 | semidirect |
| 53. #1131 | C2×C4 | semidirect |
| 54. C8×D7 | C2×C4 | semidirect |
| 60. #427 | D7 | semidirect |
| 128. C2×C8 | C4×D7 | semidirect |
| 164. C7 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6464 | 2 |
| #90214 | 2 |
| C7×#427 | 2 |
| C2×#6391 | 2 |
| #89767 | 2 |
| #89653 | 2 |
| #89632 | 2 |
| D7×#106 | 2 |
| #2912 | 7 |