Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1078 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1078 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 |
|---|---|---|
| 1. #23777805 | C2 | semidirect |
| 2. #23774391 | C2 | semidirect |
| 3. #23762704 | C2 | semidirect |
| 4. #23762688 | C2 | semidirect |
| 5. #23762035 | C2 | semidirect |
| 6. #23762010 | C2 | semidirect |
| 7. C79×#3150 | C2 | semidirect |
| 16. #19098950 | C22 | semidirect |
| 17. #19098925 | C22 | semidirect |
| 21. #19098620 | C22 | semidirect |
| 22. #19098303 | C22 | semidirect |
| 23. #19098302 | C22 | semidirect |
| 26. #532×C79 | C22 | semidirect |
| 28. #497×C79 | C22 | semidirect |
| 30. #496×C79 | C22 | semidirect |
| 31. C2×#97×C79 | C22 | semidirect |
| 193. #3150 | D79 | semidirect |
| 198. C79 | #19052 | semidirect |
| 209. #532 | C2×D79 | semidirect |
| 211. #497 | C2×D79 | semidirect |
| 214. #496 | C2×D79 | semidirect |
| 220. 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 |
| #23774391 | 2 |
| #23762704 | 2 |
| #23762688 | 2 |
| #23762035 | 2 |
| #23762010 | 2 |
| C79×#3150 | 2 |
| #19052 | 79 |