Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
344 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23765350 | C2 | semidirect |
| 3. #23764706 | C2 | semidirect |
| 4. #23761388 | C2 | semidirect |
| 5. #23761385 | C2 | semidirect |
| 6. #23761353 | C2 | semidirect |
| 7. C79×#3263 | C2 | semidirect |
| 172. #3263 | D79 | semidirect |
| 179. C79 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765350 | 2 |
| #23765345 | 2 |
| #23764706 | 2 |
| #23761388 | 2 |
| #23761385 | 2 |
| #23761353 | 2 |
| C79×#3263 | 2 |
| #12172 | 79 |