Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 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 |
|---|---|---|
| 2. #23765193 | C2 | semidirect |
| 3. #23761607 | C2 | semidirect |
| 4. #23761606 | C2 | semidirect |
| 5. #23761590 | C2 | semidirect |
| 6. #23761539 | C2 | semidirect |
| 7. C79×#1419 | C2 | semidirect |
| 89. #1419 | D79 | semidirect |
| 91. C79 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765500 | 2 |
| #23765193 | 2 |
| #23761607 | 2 |
| #23761606 | 2 |
| #23761590 | 2 |
| #23761539 | 2 |
| C79×#1419 | 2 |
| #13717 | 79 |