Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
786 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #23763335 | C2 | semidirect |
| 5. #23761972 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#2434 | C2 | semidirect |
| 141. C22⋊C4×C79 | SD16 | semidirect |
| 234. #2434 | D79 | semidirect |
| 239. C79 | #9949 | semidirect |
| 373. C22⋊C4 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| C2×#19098702 | 2 |
| #23764236 | 2 |
| #23763335 | 2 |
| #23761972 | 2 |
| #23761248 | 2 |
| C79×#2434 | 2 |
| #9949 | 79 |