Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. C2×#19097826 | C2 | semidirect |
| 4. C2×C4×#11929441 | C2 | semidirect |
| 5. #23758139 | C2 | semidirect |
| 6. #23758139 | C2 | semidirect |
| 10. C2×#14578964 | C4 | semidirect |
| 15. #19097828 | C4 | semidirect |
| 60. #11929441 | C22⋊C4 | semidirect |
| 73. C2×Dic157 | M16 | semidirect |
| 93. C2×C4×C157 | M16 | semidirect |
| 125. C157 | #1753 | semidirect |
| 215. C2×C4 | #14578964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578964 | 2 |
| C2×#19097828 | 2 |
| C2×#19097826 | 2 |
| C2×C4×#11929441 | 2 |
| #23758139 | 2 |
| #23757120 | 2 |
| #1753 | 157 |