Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C7×#103 | C2 | semidirect |
| 3. #90002 | C2 | semidirect |
| 5. C2×#6389 | C2 | semidirect |
| 7. C2×#6381 | C2 | semidirect |
| 14. C2×#1143 | C4 | semidirect |
| 59. C2×#103 | D7 | semidirect |
| 95. C7⋊C8 | C22⋊C4 | semidirect |
| 200. C7 | #1973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1143 | 2 |
| C2×C7×#103 | 2 |
| #90002 | 2 |
| C2×#6395 | 2 |
| C2×#6389 | 2 |
| #89760 | 2 |
| C2×#6381 | 2 |
| #1973 | 7 |