Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097793 | C2 | semidirect |
| 2. #23757944 | C2 | semidirect |
| 3. #23757650 | C2 | semidirect |
| 4. #23757509 | C2 | semidirect |
| 5. #23757474 | C2 | semidirect |
| 6. #23757420 | C2 | semidirect |
| 7. C4×Dic628 | C2 | semidirect |
| 8. C8×D4×C157 | C2 | semidirect |
| 38. Dic628 | D4 | semidirect |
| 87. C4×C157 | #135 | semidirect |
| 97. C157 | #3287 | semidirect |
| 106. C8×D4 | D157 | semidirect |
| 187. C4 | #19097793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| #23757944 | 2 |
| #23757650 | 2 |
| #23757509 | 2 |
| #23757474 | 2 |
| #23757420 | 2 |
| C4×Dic628 | 2 |
| C8×D4×C157 | 2 |
| #3287 | 157 |