Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19098379 | C4 | semidirect |
| 139. C79 | #12954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772268 | 2 |
| #23765174 | 2 |
| C2×#19098379 | 2 |
| #23764188 | 2 |
| #23761515 | 2 |
| #23761485 | 2 |
| C2×#362×C79 | 2 |
| #12954 | 79 |