Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23757321 | C2 | semidirect |
| 3. #23757282 | C2 | semidirect |
| 5. C2×#19097690 | C2 | semidirect |
| 6. #23757045 | C2 | semidirect |
| 105. C157 | #2049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757321 | 2 |
| #23757290 | 2 |
| #23757282 | 2 |
| #23757257 | 2 |
| C2×#19097690 | 2 |
| #23757045 | 2 |
| C2×#137×C157 | 2 |
| #2049 | 157 |