Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#14578941 | C2 | semidirect |
| 3. C2×#19097691 | C2 | semidirect |
| 4. #23757028 | C2 | semidirect |
| 5. #391×C157 | C2 | semidirect |
| 31. C2×#11929434 | D4 | semidirect |
| 35. C2×Q8×C157 | D4 | semidirect |
| 63. C2×C4×C157 | SD16 | semidirect |
| 89. C157 | #2014 | semidirect |
| 94. #391 | D157 | semidirect |
| 112. C2×Q8 | D628 | semidirect |
| 152. C2×C4 | #14578941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| C2×#19097768 | 2 |
| C2×#19097691 | 2 |
| #23757028 | 2 |
| #391×C157 | 2 |
| #2014 | 157 |