Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×C7×Q8 | C2 | semidirect |
| 3. C2×#6510 | C2 | direct (N × H) |
| 4. C22×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C22×C4×Dic7 | C2 | semidirect |
| 8. C22×C7×Q8 | C22 | semidirect |
| 14. #6510 | C22 | direct (N × H) |
| 15. C2×(C2×D7)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic7 | C22 | semidirect |
| 23. C2×C7×Q8 | C23 | semidirect |
| 32. (C2×D7)⋊C4 | C23 | semidirect |
| 33. C4×Dic7 | C23 | semidirect |
| 34. C23×Q8 | D7 | semidirect |
| 56. C22×Q8 | C2×D7 | semidirect |
| 65. C22×C7 | #124 | semidirect |
| 80. C2×Q8 | C22×D7 | semidirect |
| 91. C2×C7 | C2×#124 | semidirect |
| 110. C7 | C22×#124 | semidirect |
| 114. C22 | #6510 | direct (N × H) |
| 122. C2 | C2×#6510 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×Q8 | 2 |
| C23×D28 | 2 |
| C2×#6510 | 2 |
| C22×(C2×D7)⋊C4 | 2 |
| C22×C4×Dic7 | 2 |
| C22×#124 | 7 |