Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 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. #23761718 | C2 | semidirect |
| 3. #23761421 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 12. C2×#124×C79 | C4 | semidirect |
| 15. #393×C79 | C4 | semidirect |
| 18. #392×C79 | C4 | semidirect |
| 22. #383×C79 | C4 | semidirect |
| 203. C79 | #11730 | semidirect |
| 204. C2×#124 | Dic79 | semidirect |
| 209. #393 | Dic79 | semidirect |
| 212. #392 | Dic79 | semidirect |
| 216. #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 |
| #23761421 | 2 |
| #23761397 | 2 |
| C79×#2631 | 2 |
| #11730 | 79 |