Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#1136 | C2 | semidirect |
| 3. C7×#407 | C2 | semidirect |
| 4. C2×#6397 | C2 | semidirect |
| 5. #89349 | C2 | semidirect |
| 51. #1136 | D4 | semidirect |
| 57. #407 | D7 | semidirect |
| 116. C22×C7 | #100 | semidirect |
| 198. C7 | #1900 | semidirect |
| 211. C22 | #6397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6493 | 2 |
| C22×#1136 | 2 |
| C7×#407 | 2 |
| C2×#6397 | 2 |
| #89349 | 2 |
| #1900 | 7 |