Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1318 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #23764543 | C2 | semidirect |
| 4. #23764483 | C2 | semidirect |
| 5. #23763755 | C2 | semidirect |
| 6. #23763713 | C2 | semidirect |
| 7. #23763471 | C2 | semidirect |
| 8. C2×#541×C79 | C2 | semidirect |
| 13. C2×#14579085 | C22 | semidirect |
| 20. #19098325 | C22 | semidirect |
| 21. #19098318 | C22 | semidirect |
| 22. #19098318 | C22 | semidirect |
| 24. C2×C4⋊Q8×C79 | C22 | semidirect |
| 27. C2×#125×C79 | C22 | semidirect |
| 29. C2×C4×Q8×C79 | C22 | semidirect |
| 187. C2×#541 | D79 | semidirect |
| 195. C79 | #23942 | semidirect |
| 199. C2×C4⋊Q8 | C2×D79 | semidirect |
| 202. C2×#125 | C2×D79 | semidirect |
| 204. C2×C4×Q8 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098713 | 2 |
| #23765980 | 2 |
| #23764543 | 2 |
| #23764483 | 2 |
| #23763755 | 2 |
| #23763713 | 2 |
| #23763471 | 2 |
| C2×#541×C79 | 2 |
| #23942 | 79 |