Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
756 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 289 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. #90510 | C2 | semidirect |
| 3. #90009 | C2 | semidirect |
| 4. C2×#6407 | C2 | semidirect |
| 12. C2×#1136 | C22 | semidirect |
| 13. #6410 | C22 | semidirect |
| 14. #6407 | C22 | semidirect |
| 109. C7 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×H(5,𝔽2) | 2 |
| #90510 | 2 |
| #90009 | 2 |
| C2×#6407 | 2 |
| #2888 | 7 |