Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23764175 | C2 | semidirect |
| 3. #23762175 | C2 | semidirect |
| 6. #23761275 | C2 | semidirect |
| 7. C79×#1565 | C2 | semidirect |
| 161. #1565 | D79 | semidirect |
| 165. C79 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764240 | 2 |
| #23764175 | 2 |
| #23762175 | 2 |
| #23762067 | 2 |
| C2×#19098306 | 2 |
| #23761275 | 2 |
| C79×#1565 | 2 |
| #10603 | 79 |