Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90412 | C2 | semidirect |
| 4. #89865 | C2 | semidirect |
| 6. #89649 | C2 | semidirect |
| 7. #89645 | C2 | semidirect |
| 8. #89621 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 211. C7 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90412 | 2 |
| #90233 | 2 |
| C7×#474 | 2 |
| #89865 | 2 |
| C4×#1142 | 2 |
| #89649 | 2 |
| #89645 | 2 |
| #89621 | 2 |
| #89602 | 2 |
| #89540 | 2 |
| #89539 | 2 |
| #3364 | 7 |