Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×C7×#107 | C2 | semidirect |
| 4. C2×#6392 | C2 | semidirect |
| 5. C2×#6381 | C2 | semidirect |
| 6. D7×#107 | C2 | direct (N × H) |
| 14. C2×C8×D7 | C4 | semidirect |
| 18. C7×#107 | C22 | semidirect |
| 19. #6392 | C22 | semidirect |
| 20. #6381 | C22 | semidirect |
| 33. C2×C7×C8 | C2×C4 | semidirect |
| 40. C2×C7⋊C8 | C2×C4 | semidirect |
| 42. C8×D7 | C2×C4 | semidirect |
| 48. C2×#107 | D7 | direct (N × H) |
| 68. C7×C8 | C22×C4 | semidirect |
| 69. C7⋊C8 | C22×C4 | semidirect |
| 83. #107 | C2×D7 | direct (N × H) |
| 88. C2×D7 | #107 | direct (N × H) |
| 112. C2×C8 | C4×D7 | semidirect |
| 119. C2×C7 | C2×#107 | semidirect |
| 123. D7 | C2×#107 | direct (N × H) |
| 144. C8 | C2×C4×D7 | semidirect |
| 145. C7 | C22×#107 | semidirect |
| 161. C2 | D7×#107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D7 | 2 |
| C2×D7×C4⋊C4 | 2 |
| C2×C7×#107 | 2 |
| C2×#6392 | 2 |
| C2×#6381 | 2 |
| D7×#107 | 2 |
| C22×#107 | 7 |