Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #23761424 | C2 | semidirect |
| 4. #23761400 | C2 | semidirect |
| 12. C2×#125×C79 | C4 | semidirect |
| 14. #399×C79 | C4 | semidirect |
| 17. #397×C79 | C4 | semidirect |
| 22. #383×C79 | C4 | semidirect |
| 182. C79 | #11732 | semidirect |
| 183. C2×#125 | Dic79 | semidirect |
| 187. #399 | Dic79 | semidirect |
| 190. #397 | Dic79 | semidirect |
| 195. #383 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579076 | 2 |
| #23761718 | 2 |
| #23761424 | 2 |
| #23761400 | 2 |
| C79×#2633 | 2 |
| #11732 | 79 |