Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 54. C79⋊C16 | Q16 | semidirect |
| 102. C79 | #12462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765680 | 2 |
| #23765305 | 2 |
| #23762805 | 2 |
| #23762791 | 2 |
| #23761471 | 2 |
| #23761457 | 2 |
| C79×#1364 | 2 |
| #12462 | 79 |