Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
808 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23762558 | C2 | semidirect |
| 140. C79 | #18732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774548 | 2 |
| #23773782 | 2 |
| #23762558 | 2 |
| #23762065 | 2 |
| #23761821 | 2 |
| C79×#3556 | 2 |
| #18732 | 79 |