Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
146 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #23761476 | C2 | semidirect |
| 3. C79×#1422 | C2 | semidirect |
| 55. #1422 | D79 | semidirect |
| 57. C79 | #7448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765650 | 2 |
| #23761476 | 2 |
| C79×#1422 | 2 |
| #7448 | 79 |