Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C7×#499 | C2 | semidirect |
| 4. #89836 | C2 | semidirect |
| 5. #89836 | C2 | semidirect |
| 7. #89648 | C2 | semidirect |
| 9. #89628 | C2 | semidirect |
| 11. #89455 | C2 | semidirect |
| 65. #1131 | Q8 | semidirect |
| 66. #1131 | Q8 | semidirect |
| 74. #499 | D7 | semidirect |
| 183. C7 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90379 | 2 |
| D7×#125 | 2 |
| C7×#499 | 2 |
| #89836 | 2 |
| #89653 | 2 |
| #89648 | 2 |
| #89633 | 2 |
| #89628 | 2 |
| C4×#1131 | 2 |
| #89455 | 2 |
| #3166 | 7 |