Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#1132 | C2 | semidirect |
| 2. C2×#6464 | C2 | semidirect |
| 3. #90217 | C2 | semidirect |
| 5. C7×#427 | C2 | semidirect |
| 6. #89776 | C2 | semidirect |
| 7. #89773 | C2 | semidirect |
| 8. #89658 | C2 | semidirect |
| 9. #89636 | C2 | semidirect |
| 21. C2×#1131 | C22 | semidirect |
| 22. C2×C8×D7 | C22 | semidirect |
| 23. #6460 | C22 | semidirect |
| 31. C7×#107 | C22 | semidirect |
| 32. C7×#106 | C22 | semidirect |
| 33. #6384 | C22 | semidirect |
| 54. C2×C7×C8 | D4 | semidirect |
| 78. #427 | D7 | semidirect |
| 131. #107 | C2×D7 | semidirect |
| 132. #106 | C2×D7 | semidirect |
| 174. C2×C8 | D28 | semidirect |
| 220. C7 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1132 | 2 |
| C2×#6464 | 2 |
| #90217 | 2 |
| #90216 | 2 |
| C7×#427 | 2 |
| #89776 | 2 |
| #89773 | 2 |
| #89658 | 2 |
| #89636 | 2 |
| #3057 | 7 |