Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 12. #19098603 | C4 | semidirect |
| 13. #19098572 | C4 | semidirect |
| 198. C79 | #9362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773344 | 2 |
| #23766291 | 2 |
| #23764386 | 2 |
| #23763497 | 2 |
| #23761307 | 2 |
| #23761286 | 2 |
| C79×#1508 | 2 |
| #9362 | 79 |