Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#19097750 | C2 | semidirect |
| 3. #23757435 | C2 | semidirect |
| 4. #23757429 | C2 | semidirect |
| 5. #23757424 | C2 | semidirect |
| 6. #23757274 | C2 | semidirect |
| 7. #23757237 | C2 | semidirect |
| 9. C22×Dic314 | C22 | semidirect |
| 11. C2×#14578944 | C22 | semidirect |
| 12. C2×#14578942 | C22 | semidirect |
| 13. C2×#14578938 | C22 | semidirect |
| 17. #19097750 | C22 | semidirect |
| 18. C2×C4⋊Dic157 | C22 | semidirect |
| 21. #19097695 | C22 | semidirect |
| 22. #19097692 | C22 | semidirect |
| 24. C22⋊#11929434 | C22 | semidirect |
| 130. C22×C157 | #137 | semidirect |
| 146. C157 | #3007 | semidirect |
| 277. C22 | #19097801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C2×#19097750 | 2 |
| #23757435 | 2 |
| #23757429 | 2 |
| #23757424 | 2 |
| #23757274 | 2 |
| #23757237 | 2 |
| C22×#41×C157 | 2 |
| #3007 | 157 |