Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19098981 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. C2×#19098363 | C2 | semidirect |
| 5. #23763465 | C2 | semidirect |
| 6. #23761493 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 17. #19098834 | C4 | semidirect |
| 183. #1387 | D79 | semidirect |
| 185. C79 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098981 | 2 |
| C2×#19098834 | 2 |
| C2×#19098377 | 2 |
| C2×#19098363 | 2 |
| #23763465 | 2 |
| #23761493 | 2 |
| C79×#1387 | 2 |
| #13073 | 79 |