Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×D7×Q16 | C2 | semidirect |
| 4. C7×#462 | C2 | semidirect |
| 5. #89958 | C2 | semidirect |
| 6. #89864 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89621 | C2 | semidirect |
| 10. #89585 | C2 | semidirect |
| 11. #89580 | C2 | semidirect |
| 67. #1144 | D4 | semidirect |
| 89. #462 | D7 | semidirect |
| 109. D28 | Q16 | semidirect |
| 156. C2×D7 | C2×Q16 | semidirect |
| 161. C4×C7 | C2×Q16 | semidirect |
| 241. C7 | D4×Q16 | semidirect |
| 254. C4 | D7×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q16 | 2 |
| #90418 | 2 |
| Q8×D28 | 2 |
| C7×#462 | 2 |
| #89958 | 2 |
| #89864 | 2 |
| C4×#1144 | 2 |
| #89621 | 2 |
| #89606 | 2 |
| #89585 | 2 |
| #89580 | 2 |
| D4×Q16 | 7 |