Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. C2×#19098386 | C2 | semidirect |
| 5. #23764128 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#1376 | C2 | semidirect |
| 19. #19098374 | C4 | semidirect |
| 70. Dic316 | C4⋊C4 | semidirect |
| 74. D632 | C4⋊C4 | semidirect |
| 163. #1376 | D79 | semidirect |
| 164. C79 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098681 | 2 |
| C2×#19098386 | 2 |
| C2×#19098374 | 2 |
| #23764128 | 2 |
| #23761499 | 2 |
| C79×#1376 | 2 |
| #12950 | 79 |