Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#6554 | C2 | semidirect |
| 2. C2×C7×#131 | C2 | semidirect |
| 3. #90444 | C2 | direct (N × H) |
| 4. C2×#6472 | C2 | semidirect |
| 5. C22×Dic28 | C2 | semidirect |
| 6. C2×#6467 | C2 | semidirect |
| 9. #6554 | C22 | semidirect |
| 14. C7×#131 | C22 | semidirect |
| 17. #6472 | C22 | semidirect |
| 20. C2×Dic28 | C22 | semidirect |
| 21. #6467 | C22 | semidirect |
| 55. C2×#131 | D7 | semidirect |
| 89. #131 | C2×D7 | semidirect |
| 127. C2×C7 | #578 | semidirect |
| 149. C7 | C2×#578 | semidirect |
| 161. C2 | #90444 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6554 | 2 |
| C2×C7×#131 | 2 |
| #90444 | 2 |
| C2×#6472 | 2 |
| C22×Dic28 | 2 |
| C2×#6467 | 2 |
| C2×#578 | 7 |