Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
292 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 95 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×C8×Dic7 | C2 | semidirect |
| 4. #89757 | C2 | semidirect |
| 6. C7×#340 | C2 | semidirect |
| 7. #89324 | C2 | semidirect |
| 21. #6383 | C4 | semidirect |
| 59. #340 | D7 | semidirect |
| 205. C7 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6395 | 2 |
| C2×C8×Dic7 | 2 |
| #89760 | 2 |
| #89757 | 2 |
| C2×#6383 | 2 |
| C7×#340 | 2 |
| #89324 | 2 |
| #1934 | 7 |