Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. C7×#421 | C2 | semidirect |
| 3. #90012 | C2 | semidirect |
| 4. #89911 | C2 | semidirect |
| 5. #89894 | C2 | semidirect |
| 6. #89778 | C2 | semidirect |
| 7. #89770 | C2 | semidirect |
| 16. C2×#1144 | C4 | semidirect |
| 17. C2×#1143 | C4 | semidirect |
| 18. C2×#1142 | C4 | semidirect |
| 19. C2×#1141 | C4 | semidirect |
| 78. #421 | D7 | semidirect |
| 241. C7 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6513 | 2 |
| C7×#421 | 2 |
| #90012 | 2 |
| #89911 | 2 |
| #89894 | 2 |
| #89778 | 2 |
| #89770 | 2 |
| #1976 | 7 |