Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
998 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 159 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. #23763392 | C2 | semidirect |
| 2. #23762081 | C2 | semidirect |
| 3. #23761825 | C2 | semidirect |
| 4. #23761721 | C2 | semidirect |
| 125. D4×C79 | #100 | semidirect |
| 185. C79 | #8393 | semidirect |
| 305. D4 | #14579078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763392 | 2 |
| #23762081 | 2 |
| #23761825 | 2 |
| #23761721 | 2 |
| C2×#547×C79 | 2 |
| #8393 | 79 |