Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #23757611 | C2 | semidirect |
| 3. #23757565 | C2 | semidirect |
| 4. #23757560 | C2 | semidirect |
| 5. #23757480 | C2 | semidirect |
| 6. #23757475 | C2 | semidirect |
| 8. #23757378 | C2 | semidirect |
| 9. #23757371 | C2 | semidirect |
| 10. #23757330 | C2 | semidirect |
| 11. #533×C157 | C2 | semidirect |
| 136. C157 | #3116 | semidirect |
| 138. #533 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578954 | 2 |
| #23757611 | 2 |
| #23757565 | 2 |
| #23757560 | 2 |
| #23757480 | 2 |
| #23757475 | 2 |
| #23757433 | 2 |
| #23757378 | 2 |
| #23757371 | 2 |
| #23757330 | 2 |
| #533×C157 | 2 |
| #3116 | 157 |