Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
168 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 69 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. #89451 | C2 | semidirect |
| 5. #89279 | C2 | semidirect |
| 6. #89275 | C2 | semidirect |
| 7. #89250 | C2 | semidirect |
| 64. C7×C8 | SD16 | semidirect |
| 137. C8 | #1142 | semidirect |
| 138. C7 | #1582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D4 | 2 |
| C4×#1142 | 2 |
| #89451 | 2 |
| D4⋊(C7⋊C8) | 2 |
| #89279 | 2 |
| #89275 | 2 |
| #89250 | 2 |
| #1582 | 7 |