Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
992 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #23774407 | C2 | semidirect |
| 3. #23762705 | C2 | semidirect |
| 4. #23762035 | C2 | semidirect |
| 5. #23762010 | C2 | semidirect |
| 6. C79×#3135 | C2 | semidirect |
| 15. #19098955 | C22 | semidirect |
| 16. #19098925 | C22 | semidirect |
| 20. #19098620 | C22 | semidirect |
| 21. #19098303 | C22 | semidirect |
| 22. #19098302 | C22 | semidirect |
| 23. #533×C79 | C22 | semidirect |
| 27. #489×C79 | C22 | semidirect |
| 29. C2×#97×C79 | C22 | semidirect |
| 173. #3135 | D79 | semidirect |
| 177. C79 | #19056 | semidirect |
| 185. #533 | C2×D79 | semidirect |
| 192. #489 | C2×D79 | semidirect |
| 198. C2×#97 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23774407 | 2 |
| #23762705 | 2 |
| #23762035 | 2 |
| #23762010 | 2 |
| C79×#3135 | 2 |
| #19056 | 79 |