Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23757652 | C2 | semidirect |
| 4. #23757025 | C2 | semidirect |
| 5. #23757019 | C2 | semidirect |
| 6. #23757018 | C2 | semidirect |
| 53. D4×C157 | Q16 | semidirect |
| 78. C157 | #1669 | semidirect |
| 127. D4 | #14578944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757652 | 2 |
| #23757553 | 2 |
| D4×#11929434 | 2 |
| #23757025 | 2 |
| #23757019 | 2 |
| #23757018 | 2 |
| #474×C157 | 2 |
| #1669 | 157 |