Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23757397 | C2 | semidirect |
| 4. #23757023 | C2 | semidirect |
| 5. #23757005 | C2 | semidirect |
| 6. C8×#11929434 | C2 | semidirect |
| 24. #14578942 | C8 | semidirect |
| 42. Dic314 | C2×C8 | semidirect |
| 48. #11929434 | C2×C8 | semidirect |
| 49. #11929434 | SD16 | semidirect |
| 77. C157 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757397 | 2 |
| C4×#14578942 | 2 |
| D4×#11929434 | 2 |
| #23757023 | 2 |
| #23757005 | 2 |
| C8×#11929434 | 2 |
| D4⋊C8×C157 | 2 |
| C8×SD16 | 157 |