Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#19097794 | C2 | semidirect |
| 2. #23757934 | C2 | semidirect |
| 3. #23757658 | C2 | semidirect |
| 4. #23757511 | C2 | semidirect |
| 5. #23757509 | C2 | semidirect |
| 6. #23757497 | C2 | semidirect |
| 7. #23757434 | C2 | semidirect |
| 8. #23757412 | C2 | semidirect |
| 9. Q16×Dic157 | C2 | semidirect |
| 10. C8×C22⋊D157 | C2 | semidirect |
| 11. C22×Q16×C157 | C2 | semidirect |
| 76. Q16×C157 | D4 | semidirect |
| 113. C22×C157 | #135 | semidirect |
| 136. C157 | #3285 | semidirect |
| 139. C22×Q16 | D157 | semidirect |
| 195. Q16 | C22⋊D157 | semidirect |
| 256. C22 | #19097794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| #23757934 | 2 |
| #23757658 | 2 |
| #23757511 | 2 |
| #23757509 | 2 |
| #23757497 | 2 |
| #23757434 | 2 |
| #23757412 | 2 |
| Q16×Dic157 | 2 |
| C8×C22⋊D157 | 2 |
| C22×Q16×C157 | 2 |
| #3285 | 157 |