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. #23763133 | C2 | semidirect |
| 2. #23761734 | C2 | semidirect |
| 3. #23761424 | C2 | semidirect |
| 12. C2×C4×D4×C79 | C4 | semidirect |
| 14. #400×C79 | C4 | semidirect |
| 16. #394×C79 | C4 | semidirect |
| 22. #383×C79 | C4 | semidirect |
| 200. C79 | #11754 | semidirect |
| 201. C2×C4×D4 | Dic79 | semidirect |
| 205. #400 | Dic79 | semidirect |
| 207. #394 | Dic79 | semidirect |
| 213. #383 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763133 | 2 |
| #23761734 | 2 |
| #23761424 | 2 |
| #23761397 | 2 |
| C79×#2598 | 2 |
| #11754 | 79 |