Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C7×#547 | C2 | semidirect |
| 2. C2×#6513 | C2 | semidirect |
| 3. #90242 | C2 | semidirect |
| 4. #90011 | C2 | semidirect |
| 5. #89864 | C2 | semidirect |
| 6. #89855 | C2 | semidirect |
| 7. #89823 | C2 | semidirect |
| 8. #89819 | C2 | semidirect |
| 9. #89791 | C2 | semidirect |
| 10. C4×#1141 | C2 | semidirect |
| 11. D4×C7⋊C8 | C2 | semidirect |
| 73. #1141 | D4 | semidirect |
| 85. #547 | D7 | semidirect |
| 169. C4×C7 | #135 | semidirect |
| 251. C7 | #3283 | semidirect |
| 268. C4 | #6513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#547 | 2 |
| C2×#6513 | 2 |
| #90242 | 2 |
| #90011 | 2 |
| #89864 | 2 |
| #89855 | 2 |
| #89823 | 2 |
| #89819 | 2 |
| #89791 | 2 |
| C4×#1141 | 2 |
| D4×C7⋊C8 | 2 |
| #3283 | 7 |