Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
224 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765656 | C2 | semidirect |
| 2. #23765481 | C2 | semidirect |
| 4. #23761476 | C2 | semidirect |
| 5. #23761438 | C2 | semidirect |
| 6. #23761436 | C2 | semidirect |
| 7. C79×#2170 | C2 | semidirect |
| 111. #2170 | D79 | semidirect |
| 115. C79 | #12438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765656 | 2 |
| #23765481 | 2 |
| #23765476 | 2 |
| #23761476 | 2 |
| #23761438 | 2 |
| #23761436 | 2 |
| C79×#2170 | 2 |
| #12438 | 79 |