Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. C7×#368 | C2 | semidirect |
| 4. #89301 | C2 | semidirect |
| 5. #89288 | C2 | semidirect |
| 33. #368 | D7 | direct (N × H) |
| 80. D7 | #368 | direct (N × H) |
| 94. C7 | C2×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×C16 | 2 |
| D7×#108 | 2 |
| C7×#368 | 2 |
| #89301 | 2 |
| #89288 | 2 |
| C2×#368 | 7 |