Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×C4⋊#11929434 | C2 | semidirect |
| 3. C2×#19097700 | C2 | semidirect |
| 6. #23757027 | C2 | semidirect |
| 7. #336×C157 | C2 | semidirect |
| 43. #14578931 | C8 | semidirect |
| 72. C2×Dic157 | C2×C8 | semidirect |
| 85. C2×C4×C157 | C2×C8 | semidirect |
| 107. C2×D157 | C4⋊C8 | semidirect |
| 125. C157 | #1850 | semidirect |
| 133. #336 | D157 | semidirect |
| 209. C2×C4 | C8×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D157 | 2 |
| C2×C4⋊#11929434 | 2 |
| C2×#19097700 | 2 |
| C2×#19097683 | 2 |
| C4×#14578931 | 2 |
| #23757027 | 2 |
| #336×C157 | 2 |
| #1850 | 157 |