Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 3. #23761607 | C2 | semidirect |
| 4. #23761606 | C2 | semidirect |
| 5. #23761593 | C2 | semidirect |
| 7. C79×#1420 | C2 | semidirect |
| 85. #1420 | D79 | semidirect |
| 87. C79 | #13718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765505 | 2 |
| #23765193 | 2 |
| #23761607 | 2 |
| #23761606 | 2 |
| #23761593 | 2 |
| #23761539 | 2 |
| C79×#1420 | 2 |
| #13718 | 79 |