Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#19097794 | C2 | semidirect |
| 2. C2×#19097777 | C2 | semidirect |
| 3. #23757853 | C2 | semidirect |
| 4. #23757522 | C2 | semidirect |
| 5. #23757521 | C2 | semidirect |
| 6. #23757511 | C2 | semidirect |
| 7. #23757510 | C2 | semidirect |
| 8. #23757509 | C2 | semidirect |
| 9. #107×D157 | C2 | semidirect |
| 10. #23757273 | C2 | semidirect |
| 11. #467×C157 | C2 | semidirect |
| 65. C8×D157 | D4 | semidirect |
| 143. C157 | #3061 | semidirect |
| 151. #467 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×#19097777 | 2 |
| #23757853 | 2 |
| #23757522 | 2 |
| #23757521 | 2 |
| #23757511 | 2 |
| #23757510 | 2 |
| #23757509 | 2 |
| #107×D157 | 2 |
| #23757273 | 2 |
| #467×C157 | 2 |
| #3061 | 157 |