Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#6467 | C2 | semidirect |
| 2. C22×#1131 | C2 | semidirect |
| 3. #90215 | C2 | semidirect |
| 4. C7×#427 | C2 | semidirect |
| 5. #89774 | C2 | semidirect |
| 6. #89658 | C2 | semidirect |
| 7. #89640 | C2 | semidirect |
| 8. #89637 | C2 | semidirect |
| 14. C2×Dic28 | C22 | semidirect |
| 16. C2×D56 | C22 | semidirect |
| 17. C2×#1132 | C22 | semidirect |
| 26. C7×#107 | C22 | semidirect |
| 27. C7×#106 | C22 | semidirect |
| 28. #6384 | C22 | semidirect |
| 29. #6383 | C22 | semidirect |
| 45. C2×C7×C8 | D4 | semidirect |
| 67. #427 | D7 | semidirect |
| 112. #107 | C2×D7 | semidirect |
| 113. #106 | C2×D7 | semidirect |
| 151. C2×C8 | D28 | semidirect |
| 191. C7 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6467 | 2 |
| C22×#1131 | 2 |
| #90215 | 2 |
| C7×#427 | 2 |
| #89774 | 2 |
| #89658 | 2 |
| #89640 | 2 |
| #89637 | 2 |
| #3054 | 7 |