Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C2×C7×#127 | C2 | semidirect |
| 2. C22×#1142 | C2 | semidirect |
| 3. C22×#1141 | C2 | semidirect |
| 4. C2×#6438 | C2 | semidirect |
| 5. #89846 | C2 | direct (N × H) |
| 6. C2×#6377 | C2 | semidirect |
| 12. C7×#127 | C22 | semidirect |
| 15. C2×#1142 | C22 | semidirect |
| 17. C2×#1141 | C22 | semidirect |
| 21. #6438 | C22 | semidirect |
| 22. #6377 | C22 | semidirect |
| 46. C2×C7⋊C8 | D4 | semidirect |
| 50. C2×#127 | D7 | semidirect |
| 76. C7⋊C8 | C2×D4 | semidirect |
| 87. #127 | C2×D7 | semidirect |
| 131. C2×C7 | #496 | semidirect |
| 158. C7 | C2×#496 | semidirect |
| 174. C2 | #89846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#127 | 2 |
| C22×#1142 | 2 |
| C22×#1141 | 2 |
| C2×#6438 | 2 |
| #89846 | 2 |
| C2×#6377 | 2 |
| C2×#496 | 7 |