Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. Q8×Dic14 | C2 | semidirect |
| 3. C7×#460 | C2 | semidirect |
| 4. #89935 | C2 | semidirect |
| 5. SD16×Dic7 | C2 | semidirect |
| 6. #89842 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. #89614 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89533 | C2 | semidirect |
| 11. #89532 | C2 | semidirect |
| 82. #460 | D7 | semidirect |
| 89. C7×Q8 | #41 | semidirect |
| 111. Dic14 | SD16 | semidirect |
| 205. Q8 | #1159 | semidirect |
| 228. C7 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90409 | 2 |
| Q8×Dic14 | 2 |
| C7×#460 | 2 |
| #89935 | 2 |
| SD16×Dic7 | 2 |
| #89842 | 2 |
| C4×#1143 | 2 |
| #89614 | 2 |
| #89602 | 2 |
| #89533 | 2 |
| #89532 | 2 |
| #3362 | 7 |