Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
944 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#19098704 | C2 | semidirect |
| 3. C2×#19098298 | C2 | semidirect |
| 4. #23761670 | C2 | semidirect |
| 5. C79×#1280 | C2 | semidirect |
| 24. C22×Dic158 | D4 | semidirect |
| 49. C22⋊C8×C79 | D4 | semidirect |
| 93. C22×C4×C79 | SD16 | semidirect |
| 187. #1280 | D79 | semidirect |
| 188. C79 | #9964 | semidirect |
| 230. C22⋊C8 | D316 | semidirect |
| 269. C22×C4 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098704 | 2 |
| #23769502 | 2 |
| C2×#19098298 | 2 |
| #23761670 | 2 |
| C79×#1280 | 2 |
| #9964 | 79 |