Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×C7×#137 | C2 | semidirect |
| 3. C2×#6514 | C2 | semidirect |
| 4. C2×#6507 | C2 | semidirect |
| 5. C2×#6505 | C2 | semidirect |
| 6. C2×#6472 | C2 | semidirect |
| 7. #89962 | C2 | semidirect |
| 8. #89953 | C2 | semidirect |
| 9. #89947 | C2 | semidirect |
| 10. #89939 | C2 | semidirect |
| 11. M16×Dic7 | C2 | semidirect |
| 71. C7×M16 | D4 | semidirect |
| 85. #1136 | D4 | semidirect |
| 92. C2×#137 | D7 | semidirect |
| 183. Dic7 | #137 | semidirect |
| 218. M16 | C22⋊D7 | semidirect |
| 271. C7 | #3152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#137 | 2 |
| #90523 | 2 |
| C2×#6514 | 2 |
| C2×#6507 | 2 |
| C2×#6505 | 2 |
| C2×#6472 | 2 |
| #89962 | 2 |
| #89953 | 2 |
| #89947 | 2 |
| #89939 | 2 |
| M16×Dic7 | 2 |
| #3152 | 7 |