Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
164 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 164 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. #23761567 | C2 | semidirect |
| 2. #23761565 | C2 | semidirect |
| 7. #493×C79 | C4 | semidirect |
| 10. #322×C79 | C4 | semidirect |
| 70. C79 | #7527 | semidirect |
| 72. #493 | Dic79 | semidirect |
| 77. #322 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761567 | 2 |
| #23761565 | 2 |
| C79×#1721 | 2 |
| #7527 | 79 |