Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C7×SD32 | C2 | semidirect |
| 2. #89953 | C2 | semidirect |
| 3. C2×#6402 | C2 | semidirect |
| 5. C2×#6401 | C2 | semidirect |
| 6. C2×#6374 | C2 | semidirect |
| 7. C16×Dic7 | C2 | semidirect |
| 43. C7×C16 | D4 | semidirect |
| 44. C7⋊C16 | D4 | semidirect |
| 48. C2×SD32 | D7 | semidirect |
| 94. Dic7 | SD32 | semidirect |
| 115. C16 | C22⋊D7 | semidirect |
| 138. C7 | #2248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD32 | 2 |
| #89953 | 2 |
| C2×#6402 | 2 |
| #89923 | 2 |
| C2×#6401 | 2 |
| C2×#6374 | 2 |
| C16×Dic7 | 2 |
| #2248 | 7 |