Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
352 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 99. C42×C79 | Q16 | semidirect |
| 166. C79 | #12258 | semidirect |
| 258. C42 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769108 | 2 |
| #23762442 | 2 |
| #23762374 | 2 |
| #23761429 | 2 |
| #23761426 | 2 |
| #23761344 | 2 |
| C79×#2061 | 2 |
| #12258 | 79 |