Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23757830 | C2 | semidirect |
| 2. #23757669 | C2 | semidirect |
| 3. #23757645 | C2 | semidirect |
| 4. #23757625 | C2 | semidirect |
| 5. #23757619 | C2 | semidirect |
| 6. #23757500 | C2 | semidirect |
| 7. C4×#14578942 | C2 | semidirect |
| 8. C2×C4×#11929434 | C2 | semidirect |
| 72. #11929434 | #41 | semidirect |
| 84. C2×C4×C157 | SD16 | semidirect |
| 112. C157 | #3167 | semidirect |
| 195. C2×C4 | #14578942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757669 | 2 |
| #23757645 | 2 |
| #23757625 | 2 |
| #23757619 | 2 |
| #23757500 | 2 |
| C4×#14578942 | 2 |
| C2×C4×#11929434 | 2 |
| #532×C157 | 2 |
| #3167 | 157 |