Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 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. #23757823 | C2 | semidirect |
| 2. #23757676 | C2 | semidirect |
| 3. #23757649 | C2 | semidirect |
| 4. #23757621 | C2 | semidirect |
| 5. #23757619 | C2 | semidirect |
| 6. #23757507 | C2 | semidirect |
| 7. C4×#14578939 | C2 | semidirect |
| 8. C2×C4×#11929434 | C2 | semidirect |
| 9. #532×C157 | C2 | semidirect |
| 77. #11929434 | #41 | semidirect |
| 89. C2×C4×C157 | D8 | semidirect |
| 120. C157 | #3169 | semidirect |
| 123. #532 | D157 | semidirect |
| 208. C2×C4 | #14578939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| #23757676 | 2 |
| #23757649 | 2 |
| #23757621 | 2 |
| #23757619 | 2 |
| #23757507 | 2 |
| C4×#14578939 | 2 |
| C2×C4×#11929434 | 2 |
| #532×C157 | 2 |
| #3169 | 157 |