Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765643 | C2 | semidirect |
| 2. #23765435 | C2 | semidirect |
| 3. #23762879 | C2 | semidirect |
| 4. #23761452 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761358 | C2 | semidirect |
| 7. C79×#3355 | C2 | semidirect |
| 153. #3355 | D79 | semidirect |
| 160. C79 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765643 | 2 |
| #23765435 | 2 |
| #23762879 | 2 |
| #23761452 | 2 |
| #23761367 | 2 |
| #23761358 | 2 |
| C79×#3355 | 2 |
| #12348 | 79 |