Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#6511 | C2 | semidirect |
| 3. C2×C7×#104 | C2 | semidirect |
| 4. #89901 | C2 | semidirect |
| 5. C2×#6379 | C2 | semidirect |
| 6. #89353 | C2 | semidirect |
| 7. #89319 | C2 | semidirect |
| 16. C2×#1144 | C4 | semidirect |
| 17. C2×#1143 | C4 | semidirect |
| 18. C2×#1142 | C4 | semidirect |
| 19. C2×#1141 | C4 | semidirect |
| 73. C2×#104 | D7 | semidirect |
| 235. C7 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6513 | 2 |
| C2×#6511 | 2 |
| C2×C7×#104 | 2 |
| #89901 | 2 |
| C2×#6379 | 2 |
| #89353 | 2 |
| #89319 | 2 |
| #1876 | 7 |