Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C7×#500 | C2 | semidirect |
| 3. #89852 | C2 | semidirect |
| 7. #89650 | C2 | semidirect |
| 8. #89648 | C2 | semidirect |
| 9. #89646 | C2 | semidirect |
| 11. #89455 | C2 | semidirect |
| 67. #1131 | Q8 | semidirect |
| 68. C8×D7 | Q8 | semidirect |
| 73. #500 | D7 | semidirect |
| 195. C7 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90420 | 2 |
| C7×#500 | 2 |
| #89852 | 2 |
| #89653 | 2 |
| #89652 | 2 |
| D7×#107 | 2 |
| #89650 | 2 |
| #89648 | 2 |
| #89646 | 2 |
| #89461 | 2 |
| #89455 | 2 |
| #3164 | 7 |