Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90421 | C2 | semidirect |
| 2. #90234 | C2 | semidirect |
| 3. C7×#476 | C2 | semidirect |
| 4. #89850 | C2 | semidirect |
| 6. #89643 | C2 | semidirect |
| 7. #89630 | C2 | semidirect |
| 8. #89614 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89535 | C2 | semidirect |
| 58. #1141 | Q8 | semidirect |
| 80. #476 | D7 | semidirect |
| 216. C7 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90421 | 2 |
| #90234 | 2 |
| C7×#476 | 2 |
| #89850 | 2 |
| C4×#1141 | 2 |
| #89643 | 2 |
| #89630 | 2 |
| #89614 | 2 |
| #89602 | 2 |
| #89535 | 2 |
| #89528 | 2 |
| #3380 | 7 |