Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 125 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. #89704 | C2 | semidirect |
| 4. C4×#1136 | C2 | semidirect |
| 5. #89327 | C2 | semidirect |
| 7. C4×C7×Q8 | C4 | semidirect |
| 9. C4×C7×D4 | C4 | semidirect |
| 16. #6411 | C4 | semidirect |
| 41. C4×Dic7 | C2×C4 | semidirect |
| 43. #1136 | C2×C4 | semidirect |
| 73. C4×Q8 | Dic7 | semidirect |
| 75. C4×D4 | Dic7 | semidirect |
| 147. C7 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#41 | 2 |
| C2×#6411 | 2 |
| #89704 | 2 |
| C4×#1136 | 2 |
| #89327 | 2 |
| #1759 | 7 |