Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1170 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23774523 | C2 | semidirect |
| 3. #23768385 | C2 | semidirect |
| 4. #23762405 | C2 | semidirect |
| 5. #23761896 | C2 | semidirect |
| 6. C79×#1461 | C2 | semidirect |
| 188. #1461 | D79 | semidirect |
| 189. C79 | #18408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777171 | 2 |
| #23774523 | 2 |
| #23768385 | 2 |
| #23762405 | 2 |
| #23761896 | 2 |
| C79×#1461 | 2 |
| #18408 | 79 |