Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
396 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#6407 | C2 | semidirect |
| 3. #89696 | C2 | semidirect |
| 4. C4×#1136 | C2 | semidirect |
| 33. #1136 | D4 | semidirect |
| 77. C4×C7 | #100 | semidirect |
| 121. C7 | #1965 | semidirect |
| 129. C4 | #6407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#127 | 2 |
| C2×#6407 | 2 |
| #89696 | 2 |
| C4×#1136 | 2 |
| #1965 | 7 |