Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. C7×#556 | C2 | semidirect |
| 2. Q8×D28 | C2 | semidirect |
| 3. #89855 | C2 | semidirect |
| 4. #89853 | C2 | semidirect |
| 6. #89827 | C2 | semidirect |
| 7. #89798 | C2 | semidirect |
| 8. #89796 | C2 | semidirect |
| 9. #89793 | C2 | semidirect |
| 11. #89779 | C2 | semidirect |
| 75. #556 | D7 | semidirect |
| 222. C7 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#556 | 2 |
| Q8×D28 | 2 |
| #89855 | 2 |
| #89853 | 2 |
| #89829 | 2 |
| #89827 | 2 |
| #89798 | 2 |
| #89796 | 2 |
| #89793 | 2 |
| C4×#1141 | 2 |
| #89779 | 2 |
| #3367 | 7 |