Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23772464 | C2 | semidirect |
| 3. #23765063 | C2 | semidirect |
| 4. #23763364 | C2 | semidirect |
| 5. #23761529 | C2 | semidirect |
| 6. #23761528 | C2 | semidirect |
| 7. C79×#1794 | C2 | semidirect |
| 10. #19098746 | C4 | semidirect |
| 12. #19098736 | C4 | semidirect |
| 267. #1794 | D79 | semidirect |
| 270. C79 | #13054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772749 | 2 |
| #23772464 | 2 |
| #23765063 | 2 |
| #23763364 | 2 |
| #23761529 | 2 |
| #23761528 | 2 |
| C79×#1794 | 2 |
| #13054 | 79 |