Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. D4×#11929434 | C2 | semidirect |
| 4. #23757025 | C2 | semidirect |
| 5. #23757017 | C2 | semidirect |
| 6. #23757016 | C2 | semidirect |
| 7. #459×C157 | C2 | semidirect |
| 53. #11929434 | D8 | semidirect |
| 62. D4×C157 | D8 | semidirect |
| 92. C157 | #1667 | semidirect |
| 96. #459 | D157 | semidirect |
| 151. 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 |
| D4×#11929434 | 2 |
| #23757025 | 2 |
| #23757017 | 2 |
| #23757016 | 2 |
| #459×C157 | 2 |
| #1667 | 157 |