Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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. #89602 | C2 | semidirect |
| 5. #89274 | C2 | semidirect |
| 6. #89251 | C2 | semidirect |
| 7. #89250 | C2 | semidirect |
| 61. Dic14 | M16 | semidirect |
| 138. C7 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#1142 | 2 |
| #89784 | 2 |
| #89602 | 2 |
| C7×D4⋊C8 | 2 |
| #89274 | 2 |
| #89251 | 2 |
| #89250 | 2 |
| #1588 | 7 |