Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #90439 | C2 | semidirect |
| 2. C2×#6467 | C2 | semidirect |
| 3. C2×#6464 | C2 | semidirect |
| 4. C2×C7×#108 | C2 | semidirect |
| 5. #89904 | C2 | semidirect |
| 6. #89670 | C2 | semidirect |
| 7. #89669 | C2 | semidirect |
| 8. #89668 | C2 | semidirect |
| 18. C2×Dic28 | C22 | semidirect |
| 24. C2×D56 | C22 | semidirect |
| 25. C2×#1132 | C22 | semidirect |
| 32. C7×#108 | C22 | semidirect |
| 33. C7×#108 | C22 | semidirect |
| 34. #6398 | C22 | semidirect |
| 35. #6397 | C22 | semidirect |
| 86. C2×#108 | D7 | semidirect |
| 144. #108 | C2×D7 | semidirect |
| 145. #108 | C2×D7 | semidirect |
| 244. C7 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90439 | 2 |
| C2×#6467 | 2 |
| C2×#6464 | 2 |
| C2×C7×#108 | 2 |
| #89904 | 2 |
| #89670 | 2 |
| #89669 | 2 |
| #89668 | 2 |
| #3067 | 7 |