Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23764889 | C2 | semidirect |
| 4. #23761412 | C2 | semidirect |
| 6. #23761339 | C2 | semidirect |
| 7. C79×#2235 | C2 | semidirect |
| 154. #2235 | D79 | semidirect |
| 160. C79 | #12290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774753 | 2 |
| #23765580 | 2 |
| #23764889 | 2 |
| #23761412 | 2 |
| #23761410 | 2 |
| #23761339 | 2 |
| C79×#2235 | 2 |
| #12290 | 79 |