Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
952 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23765095 | C2 | semidirect |
| 2. #23765075 | C2 | semidirect |
| 3. #23765041 | C2 | semidirect |
| 4. #23763375 | C2 | semidirect |
| 15. C23×Q8×C79 | C4 | semidirect |
| 21. #536×C79 | C4 | semidirect |
| 24. #525×C79 | C4 | semidirect |
| 26. #519×C79 | C4 | semidirect |
| 229. C79 | #12712 | semidirect |
| 231. C23×Q8 | Dic79 | semidirect |
| 237. #536 | Dic79 | semidirect |
| 240. #525 | Dic79 | semidirect |
| 242. #519 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765095 | 2 |
| #23765075 | 2 |
| #23765041 | 2 |
| #23763375 | 2 |
| C79×#3486 | 2 |
| #12712 | 79 |