Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×C7×SD16 | C2 | semidirect |
| 2. C2×#6510 | C2 | semidirect |
| 3. C22×#1144 | C2 | semidirect |
| 4. C2×#6499 | C2 | semidirect |
| 6. C22×#1132 | C2 | semidirect |
| 7. #89940 | C2 | direct (N × H) |
| 8. C2×C8×Dic7 | C2 | semidirect |
| 14. C2×C7×SD16 | C22 | semidirect |
| 18. #6510 | C22 | semidirect |
| 20. C2×#1144 | C22 | semidirect |
| 22. #6499 | C22 | semidirect |
| 29. C2×#1132 | C22 | semidirect |
| 30. C8×Dic7 | C22 | semidirect |
| 68. C22×SD16 | D7 | semidirect |
| 114. C2×SD16 | C2×D7 | semidirect |
| 177. C2×C7 | #495 | semidirect |
| 212. C7 | C2×#495 | semidirect |
| 230. C2 | #89940 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SD16 | 2 |
| C2×#6510 | 2 |
| C22×#1144 | 2 |
| C2×#6499 | 2 |
| C22×#1141 | 2 |
| C22×#1132 | 2 |
| #89940 | 2 |
| C2×C8×Dic7 | 2 |
| C2×#495 | 7 |