Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #90161 | C2 | semidirect |
| 3. C2×C4×C7×C8 | C2 | semidirect |
| 4. #89886 | C2 | semidirect |
| 5. #89466 | C2 | semidirect |
| 6. #89465 | C2 | semidirect |
| 7. C4×#1132 | C2 | semidirect |
| 8. #89453 | C2 | semidirect |
| 9. #89452 | C2 | semidirect |
| 76. C2×C4×C8 | D7 | semidirect |
| 81. C2×C4×C7 | SD16 | semidirect |
| 100. C7×C8 | #41 | semidirect |
| 194. C2×C4 | #1132 | semidirect |
| 202. C8 | #1157 | semidirect |
| 203. C7 | #3167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90168 | 2 |
| #90161 | 2 |
| C2×C4×C7×C8 | 2 |
| #89886 | 2 |
| #89466 | 2 |
| #89465 | 2 |
| C4×#1132 | 2 |
| #89453 | 2 |
| #89452 | 2 |
| #3167 | 7 |