Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23771829 | C2 | semidirect |
| 3. #23762012 | C2 | semidirect |
| 4. #23761832 | C2 | semidirect |
| 5. #23761818 | C2 | semidirect |
| 6. #23761298 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 207. #1291 | D79 | semidirect |
| 208. C79 | #9311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773552 | 2 |
| #23771829 | 2 |
| #23762012 | 2 |
| #23761832 | 2 |
| #23761818 | 2 |
| #23761298 | 2 |
| C79×#1291 | 2 |
| #9311 | 79 |