Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
210 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 210 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. #23761563 | C2 | semidirect |
| 2. #23761437 | C2 | semidirect |
| 6. D42×C79 | C4 | semidirect |
| 9. #331×C79 | C4 | semidirect |
| 92. C79 | #7515 | semidirect |
| 93. D42 | Dic79 | semidirect |
| 98. #331 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761563 | 2 |
| #23761437 | 2 |
| C79×#1619 | 2 |
| #7515 | 79 |