Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #89842 | C2 | semidirect |
| 3. #89792 | C2 | semidirect |
| 4. #89791 | C2 | semidirect |
| 5. #89339 | C2 | semidirect |
| 6. Q8⋊(C7⋊C8) | C2 | semidirect |
| 7. D4⋊(C7⋊C8) | C2 | semidirect |
| 61. C7×Q8 | SD16 | semidirect |
| 154. Q8 | #1142 | semidirect |
| 177. C7 | #1642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#550 | 2 |
| #89842 | 2 |
| #89792 | 2 |
| #89791 | 2 |
| #89339 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| D4⋊(C7⋊C8) | 2 |
| #1642 | 7 |