Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
158 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 158 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. #23761571 | C2 | semidirect |
| 2. #23761433 | C2 | semidirect |
| 6. #562×C79 | C4 | semidirect |
| 9. #330×C79 | C4 | semidirect |
| 78. C79 | #7523 | semidirect |
| 79. #562 | Dic79 | semidirect |
| 84. #330 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761571 | 2 |
| #23761433 | 2 |
| C79×#1656 | 2 |
| #7523 | 79 |