Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#6471 | C2 | semidirect |
| 2. C22×D56 | C2 | semidirect |
| 3. C2×#6464 | C2 | semidirect |
| 4. C2×C7×#108 | C2 | semidirect |
| 5. C2×#6397 | C2 | semidirect |
| 6. #89669 | C2 | direct (N × H) |
| 13. #6471 | C22 | semidirect |
| 18. C2×D56 | C22 | semidirect |
| 21. #6464 | C22 | semidirect |
| 24. C7×#108 | C22 | semidirect |
| 25. #6397 | C22 | semidirect |
| 63. C2×#108 | D7 | semidirect |
| 111. #108 | C2×D7 | semidirect |
| 162. C2×C7 | #472 | semidirect |
| 195. C7 | C2×#472 | semidirect |
| 215. C2 | #89669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6471 | 2 |
| C22×D56 | 2 |
| C2×#6464 | 2 |
| C2×C7×#108 | 2 |
| C2×#6397 | 2 |
| #89669 | 2 |
| C2×#472 | 7 |