Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
712 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23761933 | C2 | semidirect |
| 4. #23761253 | C2 | semidirect |
| 15. C2×C4⋊Q8×C79 | C4 | semidirect |
| 16. C2×#124×C79 | C4 | semidirect |
| 20. #391×C79 | C4 | semidirect |
| 21. #390×C79 | C4 | semidirect |
| 232. C79 | #9443 | semidirect |
| 235. C2×C4⋊Q8 | Dic79 | semidirect |
| 236. C2×#124 | Dic79 | semidirect |
| 245. #391 | Dic79 | semidirect |
| 246. #390 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771845 | 2 |
| #23763318 | 2 |
| #23761933 | 2 |
| #23761253 | 2 |
| C79×#2432 | 2 |
| #9443 | 79 |