Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. C7×#498 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 5. #89850 | C2 | semidirect |
| 7. #89628 | C2 | semidirect |
| 9. #89454 | C2 | semidirect |
| 66. #1131 | Q8 | semidirect |
| 73. #498 | D7 | semidirect |
| 96. C7×C8 | C2×Q8 | semidirect |
| 97. C7⋊C8 | C2×Q8 | semidirect |
| 193. C8 | Q8×D7 | semidirect |
| 194. C7 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| D7×C4⋊Q8 | 2 |
| C7×#498 | 2 |
| #89851 | 2 |
| #89850 | 2 |
| #89633 | 2 |
| #89628 | 2 |
| C4×#1131 | 2 |
| #89454 | 2 |
| #3165 | 7 |