Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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×C7×Q32 | C2 | semidirect |
| 4. #89359 | C2 | semidirect |
| 5. #89300 | C2 | semidirect |
| 29. C2×Q32 | D7 | semidirect |
| 91. C7 | #2219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Q32 | 2 |
| #89960 | 2 |
| C2×#6372 | 2 |
| #89359 | 2 |
| #89300 | 2 |
| #2219 | 7 |