Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757820 | C2 | semidirect |
| 2. #23757677 | C2 | semidirect |
| 3. #23757648 | C2 | semidirect |
| 4. #23757618 | C2 | semidirect |
| 5. #23757510 | C2 | semidirect |
| 6. #23757508 | C2 | semidirect |
| 7. #23757506 | C2 | semidirect |
| 8. C4×D1256 | C2 | semidirect |
| 9. C4×#14578939 | C2 | semidirect |
| 10. C4×C8×D157 | C2 | semidirect |
| 11. C4×D8×C157 | C2 | semidirect |
| 89. C4×D157 | D8 | semidirect |
| 91. #11929434 | #41 | semidirect |
| 101. C8×C157 | #41 | semidirect |
| 127. C157 | #3169 | semidirect |
| 138. C4×D8 | D157 | semidirect |
| 229. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757820 | 2 |
| #23757677 | 2 |
| #23757648 | 2 |
| #23757618 | 2 |
| #23757510 | 2 |
| #23757508 | 2 |
| #23757506 | 2 |
| C4×D1256 | 2 |
| C4×#14578939 | 2 |
| C4×C8×D157 | 2 |
| C4×D8×C157 | 2 |
| #3169 | 157 |