Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #23762770 | C2 | semidirect |
| 4. #23761472 | C2 | semidirect |
| 5. #23761450 | C2 | semidirect |
| 7. C79×#2183 | C2 | semidirect |
| 70. C16×C79 | SD16 | semidirect |
| 111. #2183 | D79 | semidirect |
| 117. C79 | #12444 | semidirect |
| 180. C16 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765656 | 2 |
| #23762770 | 2 |
| #23762760 | 2 |
| #23761472 | 2 |
| #23761450 | 2 |
| #23761447 | 2 |
| C79×#2183 | 2 |
| #12444 | 79 |