Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 15. #19098380 | C4 | semidirect |
| 149. C79 | #13135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098380 | 2 |
| #23765119 | 2 |
| #23764259 | 2 |
| #23763281 | 2 |
| #23761508 | 2 |
| #23761481 | 2 |
| C79×#2159 | 2 |
| #13135 | 79 |