Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. C4×C7×Q16 | C2 | semidirect |
| 4. #89958 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89793 | C2 | semidirect |
| 7. #89656 | C2 | semidirect |
| 8. #89585 | C2 | semidirect |
| 9. D7×#103 | C2 | semidirect |
| 11. #89453 | C2 | semidirect |
| 85. C4×Q16 | D7 | semidirect |
| 103. D28 | Q16 | semidirect |
| 225. C7 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90270 | 2 |
| Q8×D28 | 2 |
| C4×C7×Q16 | 2 |
| #89958 | 2 |
| #89803 | 2 |
| #89793 | 2 |
| #89656 | 2 |
| #89585 | 2 |
| D7×#103 | 2 |
| C8×D28 | 2 |
| #89453 | 2 |
| #3299 | 7 |