Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C7×D8 | C2 | semidirect |
| 2. #90496 | C2 | semidirect |
| 3. C2×#6464 | C2 | semidirect |
| 4. #89987 | C2 | semidirect |
| 5. #89931 | C2 | semidirect |
| 6. #89929 | C2 | semidirect |
| 7. #89878 | C2 | semidirect |
| 16. #6501 | C22 | semidirect |
| 21. C2×#1131 | C22 | semidirect |
| 22. C2×C8×D7 | C22 | semidirect |
| 23. #6406 | C22 | semidirect |
| 24. #6392 | C22 | semidirect |
| 25. #6391 | C22 | semidirect |
| 42. C2×C7×C8 | D4 | semidirect |
| 53. C22×D8 | D7 | semidirect |
| 133. C2×C8 | C22⋊D7 | semidirect |
| 168. C7 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D8 | 2 |
| #90496 | 2 |
| C2×#6464 | 2 |
| #89987 | 2 |
| #89931 | 2 |
| #89929 | 2 |
| #89878 | 2 |
| #3058 | 7 |