Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 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. #23757676 | C2 | semidirect |
| 3. #23757647 | C2 | semidirect |
| 4. #23757645 | C2 | semidirect |
| 5. #23757620 | C2 | semidirect |
| 6. C8×#11929434 | C2 | semidirect |
| 7. #486×C157 | C2 | semidirect |
| 46. #11929434 | D8 | semidirect |
| 47. #11929434 | SD16 | semidirect |
| 75. C157 | #1706 | semidirect |
| 82. #486 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757676 | 2 |
| #23757649 | 2 |
| #23757647 | 2 |
| #23757645 | 2 |
| #23757620 | 2 |
| C8×#11929434 | 2 |
| #486×C157 | 2 |
| #1706 | 157 |