Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×C7×C4⋊C8 | C2 | semidirect |
| 4. C2×#6390 | C2 | semidirect |
| 6. #89701 | C2 | semidirect |
| 7. #89346 | C2 | semidirect |
| 61. C2×C4⋊C8 | D7 | semidirect |
| 80. C2×C4×C7 | SD16 | semidirect |
| 218. C2×C4 | #1132 | semidirect |
| 227. C7 | #2055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1132 | 2 |
| C2×C7×C4⋊C8 | 2 |
| C2×#6395 | 2 |
| C2×#6390 | 2 |
| #89711 | 2 |
| #89701 | 2 |
| #89346 | 2 |
| #2055 | 7 |