Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1254 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23774521 | C2 | semidirect |
| 3. #23762385 | C2 | semidirect |
| 4. #23761894 | C2 | semidirect |
| 5. #23761721 | C2 | semidirect |
| 6. C79×#2547 | C2 | semidirect |
| 17. #19098876 | C22 | semidirect |
| 19. #19098616 | C22 | semidirect |
| 20. #19098296 | C22 | semidirect |
| 21. #19098287 | C22 | semidirect |
| 22. C2×C4⋊Q8×C79 | C22 | semidirect |
| 25. #397×C79 | C22 | semidirect |
| 28. C4×C4⋊C4×C79 | C22 | semidirect |
| 199. #2547 | D79 | semidirect |
| 203. C79 | #18394 | semidirect |
| 211. C2×C4⋊Q8 | C2×D79 | semidirect |
| 220. #397 | C2×D79 | semidirect |
| 223. C4×C4⋊C4 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777164 | 2 |
| #23774521 | 2 |
| #23762385 | 2 |
| #23761894 | 2 |
| #23761721 | 2 |
| C79×#2547 | 2 |
| #18394 | 79 |