Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #23764188 | C2 | semidirect |
| 5. #23761511 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C2×#368×C79 | C2 | semidirect |
| 17. #19098371 | C4 | semidirect |
| 142. C2×#368 | D79 | semidirect |
| 148. C79 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772316 | 2 |
| #23765127 | 2 |
| C2×#19098371 | 2 |
| #23764188 | 2 |
| #23761511 | 2 |
| #23761488 | 2 |
| C2×#368×C79 | 2 |
| #12947 | 79 |