Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23762168 | C2 | semidirect |
| 4. #23762167 | C2 | semidirect |
| 6. #23761293 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 24. #19098302 | C4 | semidirect |
| 25. #19098302 | C4 | semidirect |
| 26. #19098302 | C4 | semidirect |
| 27. #19098302 | C4 | semidirect |
| 193. #1300 | D79 | semidirect |
| 194. C79 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772470 | 2 |
| #23764232 | 2 |
| #23762168 | 2 |
| #23762167 | 2 |
| #23761991 | 2 |
| #23761293 | 2 |
| C79×#1300 | 2 |
| #8918 | 79 |