Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23773923 | C2 | semidirect |
| 5. #23761507 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 7. C79×#1386 | C2 | semidirect |
| 29. C2×D632 | Q8 | semidirect |
| 154. #1386 | D79 | semidirect |
| 156. C79 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773923 | 2 |
| #23765117 | 2 |
| #23765115 | 2 |
| #23764274 | 2 |
| #23761507 | 2 |
| #23761483 | 2 |
| C79×#1386 | 2 |
| #13367 | 79 |