Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
532 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C4×#14579076 | C2 | semidirect |
| 2. #23761741 | C2 | semidirect |
| 3. #23761400 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 13. C2×#121×C79 | C4 | semidirect |
| 15. #398×C79 | C4 | semidirect |
| 17. #394×C79 | C4 | semidirect |
| 22. C2×#95×C79 | C4 | semidirect |
| 205. C79 | #11775 | semidirect |
| 207. C2×#121 | Dic79 | semidirect |
| 211. #398 | Dic79 | semidirect |
| 213. #394 | Dic79 | semidirect |
| 219. C2×#95 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579076 | 2 |
| #23761741 | 2 |
| #23761400 | 2 |
| #23761397 | 2 |
| C79×#2543 | 2 |
| #11775 | 79 |