Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
374 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #23774834 | C2 | semidirect |
| 2. #23765312 | C2 | semidirect |
| 3. #23764653 | C2 | semidirect |
| 4. #23761416 | C2 | semidirect |
| 5. #23761415 | C2 | semidirect |
| 6. #23761341 | C2 | semidirect |
| 7. C79×#2184 | C2 | semidirect |
| 175. #2184 | D79 | semidirect |
| 180. C79 | #12164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774834 | 2 |
| #23765312 | 2 |
| #23764653 | 2 |
| #23761416 | 2 |
| #23761415 | 2 |
| #23761341 | 2 |
| C79×#2184 | 2 |
| #12164 | 79 |