Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×Q16 | C2 | semidirect |
| 2. #90507 | C2 | semidirect |
| 3. C2×#6505 | C2 | semidirect |
| 5. #89963 | C2 | semidirect |
| 6. #89962 | C2 | semidirect |
| 7. #89953 | C2 | semidirect |
| 8. #89873 | C2 | semidirect |
| 62. C22×Q16 | D7 | semidirect |
| 177. C7 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| #90507 | 2 |
| C2×#6505 | 2 |
| C2×#6467 | 2 |
| #89963 | 2 |
| #89962 | 2 |
| #89953 | 2 |
| #89873 | 2 |
| #3156 | 7 |