Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 18. C2×C4⋊C4×C79 | C8 | semidirect |
| 114. C79 | #7132 | semidirect |
| 128. C2×C4⋊C4 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761243 | 2 |
| C79×#1445 | 2 |
| #7132 | 79 |