Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23762117 | C2 | semidirect |
| 5. #23761257 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1556 | C2 | semidirect |
| 195. #1556 | D79 | semidirect |
| 199. C79 | #9453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772428 | 2 |
| #23768574 | 2 |
| #23762117 | 2 |
| #23761740 | 2 |
| #23761257 | 2 |
| #23761255 | 2 |
| C79×#1556 | 2 |
| #9453 | 79 |