Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 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. C2×C7×M32 | C2 | semidirect |
| 3. C2×#6386 | C2 | semidirect |
| 4. #89309 | C2 | direct (N × H) |
| 15. C7×M32 | C22 | semidirect |
| 18. #6386 | C22 | semidirect |
| 47. C2×M32 | D7 | semidirect |
| 84. M32 | C2×D7 | semidirect |
| 126. C2×C7 | #349 | semidirect |
| 152. C7 | C2×#349 | semidirect |
| 169. C2 | #89309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1131 | 2 |
| C2×C7×M32 | 2 |
| C2×#6386 | 2 |
| #89309 | 2 |
| C2×#349 | 7 |