Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×M32 | C2 | semidirect |
| 3. C2×D7×C16 | C2 | semidirect |
| 4. C22⋊(C7⋊C16) | C2 | semidirect |
| 5. (C2×D7)⋊C16 | C2 | semidirect |
| 6. #89297 | C2 | semidirect |
| 7. Dic7⋊C16 | C2 | semidirect |
| 38. C7×C16 | D4 | semidirect |
| 41. C2×M32 | D7 | semidirect |
| 84. C2×D7 | M32 | semidirect |
| 109. C16 | C22⋊D7 | semidirect |
| 132. C7 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M32 | 2 |
| C8×C22⋊D7 | 2 |
| C2×D7×C16 | 2 |
| C22⋊(C7⋊C16) | 2 |
| (C2×D7)⋊C16 | 2 |
| #89297 | 2 |
| Dic7⋊C16 | 2 |
| #2168 | 7 |