Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757989 | C2 | semidirect |
| 2. #23757926 | C2 | semidirect |
| 3. #23757599 | C2 | semidirect |
| 4. #23757593 | C2 | semidirect |
| 5. #23757560 | C2 | semidirect |
| 6. #23757550 | C2 | semidirect |
| 7. #23757527 | C2 | semidirect |
| 8. C4×D1256 | C2 | semidirect |
| 9. #23757352 | C2 | semidirect |
| 10. #23757312 | C2 | semidirect |
| 11. #498×C157 | C2 | semidirect |
| 101. C8×C157 | #41 | semidirect |
| 127. C157 | #3354 | semidirect |
| 131. #498 | D157 | semidirect |
| 229. C8 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757989 | 2 |
| #23757926 | 2 |
| #23757599 | 2 |
| #23757593 | 2 |
| #23757560 | 2 |
| #23757550 | 2 |
| #23757527 | 2 |
| C4×D1256 | 2 |
| #23757352 | 2 |
| #23757312 | 2 |
| #498×C157 | 2 |
| #3354 | 157 |