Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19097792 | C2 | semidirect |
| 2. #23757824 | C2 | semidirect |
| 3. C4×#14578953 | C2 | semidirect |
| 4. #23757498 | C2 | semidirect |
| 5. #23757490 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757474 | C2 | semidirect |
| 8. #23757468 | C2 | semidirect |
| 9. C4⋊C8×D157 | C2 | semidirect |
| 10. #23757268 | C2 | semidirect |
| 11. #461×C157 | C2 | semidirect |
| 47. #14578953 | D4 | semidirect |
| 136. C4×C157 | #135 | semidirect |
| 150. C157 | #3035 | semidirect |
| 158. #461 | D157 | semidirect |
| 292. C4 | #19097792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097792 | 2 |
| #23757824 | 2 |
| C4×#14578953 | 2 |
| #23757498 | 2 |
| #23757490 | 2 |
| #23757480 | 2 |
| #23757474 | 2 |
| #23757468 | 2 |
| C4⋊C8×D157 | 2 |
| #23757268 | 2 |
| #461×C157 | 2 |
| #3035 | 157 |