Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097691 | C2 | semidirect |
| 3. C2×C4×#11929434 | C2 | semidirect |
| 4. #384×C157 | C2 | semidirect |
| 9. #19097768 | C4 | semidirect |
| 25. C2×#11929434 | D4 | semidirect |
| 63. C4×C157 | #102 | semidirect |
| 72. C157 | #1957 | semidirect |
| 77. #384 | D157 | semidirect |
| 136. C4 | #19097691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097768 | 2 |
| C2×#19097691 | 2 |
| C2×C4×#11929434 | 2 |
| #384×C157 | 2 |
| #1957 | 157 |