Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23764752 | C2 | semidirect |
| 3. #23762425 | C2 | semidirect |
| 4. #23761425 | C2 | semidirect |
| 6. #23761349 | C2 | semidirect |
| 204. C79 | #12231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771499 | 2 |
| #23764752 | 2 |
| #23762425 | 2 |
| #23761425 | 2 |
| #23761397 | 2 |
| #23761349 | 2 |
| C79×#1596 | 2 |
| #12231 | 79 |