Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23773952 | C2 | semidirect |
| 3. #23773223 | C2 | semidirect |
| 4. #23769345 | C2 | semidirect |
| 5. #23764611 | C2 | semidirect |
| 6. #23764380 | C2 | semidirect |
| 7. #23763612 | C2 | semidirect |
| 8. #23763213 | C2 | semidirect |
| 9. C79×#1965 | C2 | semidirect |
| 134. M16×C79 | #41 | semidirect |
| 206. #1965 | D79 | semidirect |
| 209. C79 | #25690 | semidirect |
| 314. M16 | #11929623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777274 | 2 |
| #23773952 | 2 |
| #23773223 | 2 |
| #23769345 | 2 |
| #23764611 | 2 |
| #23764380 | 2 |
| #23763612 | 2 |
| #23763213 | 2 |
| C79×#1965 | 2 |
| #25690 | 79 |