Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23758090 | C2 | semidirect |
| 2. #23758087 | C2 | semidirect |
| 3. #23757653 | C2 | semidirect |
| 4. #23757549 | C2 | semidirect |
| 5. #23757548 | C2 | semidirect |
| 6. #23757457 | C2 | semidirect |
| 7. #23757391 | C2 | semidirect |
| 8. #443×C157 | C2 | semidirect |
| 99. C157 | #3293 | semidirect |
| 108. #443 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758090 | 2 |
| #23758087 | 2 |
| #23757653 | 2 |
| #23757549 | 2 |
| #23757548 | 2 |
| #23757457 | 2 |
| #23757391 | 2 |
| #443×C157 | 2 |
| #3293 | 157 |