Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765172 | C2 | semidirect |
| 5. #23763523 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C79×#2158 | C2 | semidirect |
| 141. #2158 | D79 | semidirect |
| 148. C79 | #13525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765172 | 2 |
| #23765135 | 2 |
| C2×#19098371 | 2 |
| #23764296 | 2 |
| #23763523 | 2 |
| #23761488 | 2 |
| C79×#2158 | 2 |
| #13525 | 79 |