Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. C2×#6410 | C2 | semidirect |
| 5. C2×#6409 | C2 | semidirect |
| 6. C2×#6396 | C2 | semidirect |
| 7. #89349 | C2 | semidirect |
| 197. C7 | #2052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#137 | 2 |
| #90006 | 2 |
| #90004 | 2 |
| C2×#6410 | 2 |
| C2×#6409 | 2 |
| C2×#6396 | 2 |
| #89349 | 2 |
| #2052 | 7 |