Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #23757025 | C2 | semidirect |
| 5. #23757024 | C2 | semidirect |
| 6. #23757023 | C2 | semidirect |
| 7. #335×C157 | C2 | semidirect |
| 53. #11929434 | M16 | semidirect |
| 60. C8×C157 | M16 | semidirect |
| 77. C157 | #1569 | semidirect |
| 83. #335 | D157 | semidirect |
| 138. C8 | #14578937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757329 | 2 |
| #23757295 | 2 |
| C4×#14578937 | 2 |
| #23757025 | 2 |
| #23757024 | 2 |
| #23757023 | 2 |
| #335×C157 | 2 |
| #1569 | 157 |