Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 131. C79 | #13491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098378 | 2 |
| #23765119 | 2 |
| #23764315 | 2 |
| #23761516 | 2 |
| #23761511 | 2 |
| #23761486 | 2 |
| C79×#1833 | 2 |
| #13491 | 79 |