Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #23764344 | C2 | semidirect |
| 4. #23761911 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 11. #19098844 | C4 | semidirect |
| 12. #19098769 | C4 | semidirect |
| 187. #1300 | D79 | semidirect |
| 189. C79 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773500 | 2 |
| #23766044 | 2 |
| #23764344 | 2 |
| #23761911 | 2 |
| #23761844 | 2 |
| #23761257 | 2 |
| C79×#1300 | 2 |
| #9327 | 79 |