Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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×SD16 | C2 | semidirect |
| 2. C2×#6510 | C2 | semidirect |
| 4. C2×#6409 | C2 | semidirect |
| 5. #89993 | C2 | semidirect |
| 6. C2×#6395 | C2 | semidirect |
| 7. #89345 | C2 | semidirect |
| 66. C22×SD16 | D7 | semidirect |
| 237. C7 | #2012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SD16 | 2 |
| C2×#6510 | 2 |
| C22×#1141 | 2 |
| C2×#6409 | 2 |
| #89993 | 2 |
| C2×#6395 | 2 |
| #89345 | 2 |
| #2012 | 7 |