Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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. #90168 | C2 | semidirect |
| 2. C4×#1157 | C2 | semidirect |
| 3. C7×#431 | C2 | semidirect |
| 4. #89622 | C2 | semidirect |
| 5. #89620 | C2 | semidirect |
| 6. #89615 | C2 | semidirect |
| 7. #89614 | C2 | semidirect |
| 8. #89509 | C2 | semidirect |
| 9. #89506 | C2 | semidirect |
| 10. C4×D56 | C2 | semidirect |
| 11. C4×#1132 | C2 | semidirect |
| 94. #431 | D7 | semidirect |
| 119. D28 | #41 | semidirect |
| 126. Dic14 | #41 | semidirect |
| 261. C7 | #3106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90168 | 2 |
| C4×#1157 | 2 |
| C7×#431 | 2 |
| #89622 | 2 |
| #89620 | 2 |
| #89615 | 2 |
| #89614 | 2 |
| #89509 | 2 |
| #89506 | 2 |
| C4×D56 | 2 |
| C4×#1132 | 2 |
| #3106 | 7 |