Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14578942 | C2 | semidirect |
| 2. #23757844 | C2 | semidirect |
| 3. #23757748 | C2 | semidirect |
| 4. #23757486 | C2 | semidirect |
| 5. #23757476 | C2 | semidirect |
| 6. #23757301 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 8. #23757269 | C2 | semidirect |
| 14. #19097769 | C22 | semidirect |
| 15. #19097758 | C22 | semidirect |
| 23. #19097700 | C22 | semidirect |
| 24. #19097696 | C22 | semidirect |
| 25. #19097695 | C22 | semidirect |
| 26. #19097692 | C22 | semidirect |
| 116. C157 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578942 | 2 |
| #23757844 | 2 |
| #23757748 | 2 |
| #23757486 | 2 |
| #23757476 | 2 |
| #23757301 | 2 |
| #23757283 | 2 |
| #23757269 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3042 | 157 |