Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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×#533 | C2 | semidirect |
| 3. #89861 | C2 | semidirect |
| 4. #89858 | C2 | semidirect |
| 5. #89822 | C2 | semidirect |
| 7. #89800 | C2 | semidirect |
| 8. #89698 | C2 | semidirect |
| 11. C7×C4⋊Q8 | C22 | semidirect |
| 12. C7×C4⋊Q8 | C22 | semidirect |
| 17. C4×C7×Q8 | C22 | semidirect |
| 20. C2×#1144 | C22 | semidirect |
| 29. #6384 | C22 | semidirect |
| 31. C4⋊(C7⋊C8) | C22 | semidirect |
| 32. #6377 | C22 | semidirect |
| 66. #533 | D7 | semidirect |
| 103. C4⋊Q8 | C2×D7 | semidirect |
| 104. C4⋊Q8 | C2×D7 | semidirect |
| 113. C4×Q8 | C2×D7 | semidirect |
| 202. C7 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| C2×#6438 | 2 |
| #89861 | 2 |
| #89858 | 2 |
| #89822 | 2 |
| #89818 | 2 |
| #89800 | 2 |
| #89698 | 2 |
| #3215 | 7 |