Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #90207 | C2 | semidirect |
| 4. C7×#427 | C2 | semidirect |
| 5. #89873 | C2 | semidirect |
| 6. #89776 | C2 | semidirect |
| 8. #89661 | C2 | semidirect |
| 9. #89624 | C2 | semidirect |
| 17. C2×#1132 | C4 | semidirect |
| 21. #6450 | C22 | semidirect |
| 26. C7×#107 | C22 | semidirect |
| 27. C7×#106 | C22 | semidirect |
| 28. #6389 | C22 | semidirect |
| 29. C8×Dic7 | C22 | semidirect |
| 30. #6384 | C22 | semidirect |
| 43. C2×Dic14 | C2×C4 | semidirect |
| 45. C2×C7×C8 | C2×C4 | semidirect |
| 62. #1132 | C2×C4 | semidirect |
| 63. #1132 | C2×C4 | semidirect |
| 69. #427 | D7 | semidirect |
| 112. #107 | C2×D7 | semidirect |
| 113. #106 | C2×D7 | semidirect |
| 147. C2×C8 | C4×D7 | semidirect |
| 189. C7 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1132 | 2 |
| #90212 | 2 |
| #90207 | 2 |
| C7×#427 | 2 |
| #89873 | 2 |
| #89776 | 2 |
| #89773 | 2 |
| #89661 | 2 |
| #89624 | 2 |
| #2949 | 7 |