Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23768624 | C2 | semidirect |
| 5. #23761267 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C79×#1294 | C2 | semidirect |
| 227. #1294 | D79 | semidirect |
| 230. C79 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768624 | 2 |
| #23764235 | 2 |
| #23761969 | 2 |
| C2×#19098296 | 2 |
| #23761267 | 2 |
| #23761247 | 2 |
| C79×#1294 | 2 |
| #10376 | 79 |