Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23757649 | C2 | semidirect |
| 2. #23757468 | C2 | semidirect |
| 3. #23757017 | C2 | semidirect |
| 4. D4⋊#11929434 | C2 | semidirect |
| 5. D42×C157 | C2 | semidirect |
| 8. #19097768 | C22 | semidirect |
| 9. C4⋊#11929434 | C22 | semidirect |
| 11. C4×#11929434 | C22 | semidirect |
| 50. D4×C157 | D8 | semidirect |
| 74. C157 | #1619 | semidirect |
| 76. D42 | D157 | semidirect |
| 123. D4 | #14578939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757649 | 2 |
| #23757468 | 2 |
| #23757017 | 2 |
| D4⋊#11929434 | 2 |
| D42×C157 | 2 |
| #1619 | 157 |