Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
682 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23762064 | C2 | semidirect |
| 3. #23762037 | C2 | semidirect |
| 4. #23761835 | C2 | semidirect |
| 5. #23761832 | C2 | semidirect |
| 6. #23761752 | C2 | semidirect |
| 7. C79×#1469 | C2 | semidirect |
| 270. #1469 | D79 | semidirect |
| 271. C79 | #8477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777294 | 2 |
| #23762064 | 2 |
| #23762037 | 2 |
| #23761835 | 2 |
| #23761832 | 2 |
| #23761752 | 2 |
| C79×#1469 | 2 |
| #8477 | 79 |