Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 177. C79 | #10115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774345 | 2 |
| #23773782 | 2 |
| #23764388 | 2 |
| #23761995 | 2 |
| #23761821 | 2 |
| #23761289 | 2 |
| C79×#3255 | 2 |
| #10115 | 79 |