Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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. C2×C7×#135 | C2 | semidirect |
| 2. #90524 | C2 | semidirect |
| 3. C2×#6464 | C2 | semidirect |
| 4. #90004 | C2 | semidirect |
| 5. #89961 | C2 | semidirect |
| 6. #89943 | C2 | semidirect |
| 7. #89931 | C2 | semidirect |
| 8. C2×#6391 | C2 | semidirect |
| 49. C2×C7×C8 | D4 | semidirect |
| 61. C2×#135 | D7 | semidirect |
| 152. C2×C8 | C22⋊D7 | semidirect |
| 191. C7 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#135 | 2 |
| #90524 | 2 |
| C2×#6464 | 2 |
| #90004 | 2 |
| #89961 | 2 |
| #89943 | 2 |
| #89931 | 2 |
| C2×#6391 | 2 |
| #3060 | 7 |