Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 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. #23757830 | C2 | semidirect |
| 4. #23757045 | C2 | semidirect |
| 5. #23757033 | C2 | semidirect |
| 6. #23757030 | C2 | semidirect |
| 42. C2×Q8×C157 | Q8 | semidirect |
| 44. C2×D4×C157 | Q8 | semidirect |
| 101. C157 | #2031 | semidirect |
| 130. C2×Q8 | Dic314 | semidirect |
| 132. C2×D4 | Dic314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757290 | 2 |
| #23757247 | 2 |
| #23757045 | 2 |
| #23757033 | 2 |
| #23757030 | 2 |
| C2×#104×C157 | 2 |
| #2031 | 157 |