Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
148 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 27 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 |
|---|---|---|
| 1. #23761569 | C2 | semidirect |
| 2. #23761439 | C2 | semidirect |
| 76. C79 | #7521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761569 | 2 |
| #23761439 | 2 |
| C79×#1634 | 2 |
| #7521 | 79 |