Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #90523 | C2 | semidirect |
| 3. C2×#6514 | C2 | semidirect |
| 4. C2×#6499 | C2 | semidirect |
| 5. C2×#6495 | C2 | semidirect |
| 6. C2×#6472 | C2 | semidirect |
| 7. #89940 | C2 | semidirect |
| 8. #89939 | C2 | semidirect |
| 9. #89927 | C2 | semidirect |
| 10. #89926 | C2 | semidirect |
| 11. M16×Dic7 | C2 | semidirect |
| 22. #6510 | C22 | semidirect |
| 23. #6507 | C22 | semidirect |
| 24. C2×#1144 | C22 | semidirect |
| 25. #6503 | C22 | semidirect |
| 30. #6499 | C22 | semidirect |
| 32. C2×#1142 | C22 | semidirect |
| 39. C2×Dic28 | C22 | semidirect |
| 40. C2×#1132 | C22 | semidirect |
| 41. #6389 | C22 | semidirect |
| 42. C8×Dic7 | C22 | semidirect |
| 71. C7×M16 | D4 | semidirect |
| 85. #1136 | D4 | semidirect |
| 92. C2×AGL(1,ℤ/8) | D7 | semidirect |
| 221. M16 | C22⋊D7 | semidirect |
| 276. C7 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×AGL(1,ℤ/8) | 2 |
| #90523 | 2 |
| C2×#6514 | 2 |
| C2×#6499 | 2 |
| C2×#6495 | 2 |
| C2×#6472 | 2 |
| #89940 | 2 |
| #89939 | 2 |
| #89927 | 2 |
| #89926 | 2 |
| M16×Dic7 | 2 |
| #3153 | 7 |