Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
182 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 65 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. C7×C8×D4 | C2 | semidirect |
| 3. #89460 | C2 | semidirect |
| 4. D4⋊(C7⋊C8) | C2 | semidirect |
| 5. #89278 | C2 | semidirect |
| 6. #89275 | C2 | semidirect |
| 7. #89249 | C2 | semidirect |
| 45. C8×D4 | D7 | semidirect |
| 53. C7×D4 | M16 | semidirect |
| 130. D4 | #1131 | semidirect |
| 147. C7 | #1586 | 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×#1141 | 2 |
| #89460 | 2 |
| D4⋊(C7⋊C8) | 2 |
| #89278 | 2 |
| #89275 | 2 |
| #89249 | 2 |
| #1586 | 7 |