Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
310 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 144. C79 | #10632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764219 | 2 |
| #23763574 | 2 |
| #23762073 | 2 |
| #23762071 | 2 |
| #23761258 | 2 |
| #23761244 | 2 |
| C79×#1286 | 2 |
| #10632 | 79 |