Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 198. C79 | #10011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774602 | 2 |
| #23768788 | 2 |
| #23764345 | 2 |
| #23762003 | 2 |
| #23761847 | 2 |
| #23761255 | 2 |
| C79×#3113 | 2 |
| #10011 | 79 |