Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #23773953 | C2 | semidirect |
| 3. #23773223 | C2 | semidirect |
| 4. #23769343 | C2 | semidirect |
| 5. #23764613 | C2 | semidirect |
| 6. #23764239 | C2 | semidirect |
| 7. #23763611 | C2 | semidirect |
| 8. #23763211 | C2 | semidirect |
| 9. C79×#1995 | C2 | semidirect |
| 109. #11929608 | #41 | semidirect |
| 205. #1995 | D79 | semidirect |
| 209. C79 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777277 | 2 |
| #23773953 | 2 |
| #23773223 | 2 |
| #23769343 | 2 |
| #23764613 | 2 |
| #23764239 | 2 |
| #23763611 | 2 |
| #23763211 | 2 |
| C79×#1995 | 2 |
| #25690 | 79 |