Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19097801 | C2 | semidirect |
| 2. C22×Dic628 | C2 | semidirect |
| 3. #23757844 | C2 | semidirect |
| 4. #23757664 | C2 | semidirect |
| 5. #23757656 | C2 | semidirect |
| 6. #23757651 | C2 | semidirect |
| 7. #23757228 | C2 | semidirect |
| 96. C157 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C22×Dic628 | 2 |
| #23757844 | 2 |
| #23757664 | 2 |
| #23757656 | 2 |
| #23757651 | 2 |
| #23757228 | 2 |
| C2×#135×C157 | 2 |
| #3156 | 157 |