Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
5150 conjugacy classes of subgroups; only the 2363 normal subgroups are shown.
This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 2363 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×#19098408 | C2 | direct (N × H) |
| 7. C22×C4×Dic79 | C4 | semidirect |
| 9. #19098408 | C22 | direct (N × H) |
| 19. C2×C4×Dic79 | C2×C4 | semidirect |
| 35. C4×Dic79 | C22×C4 | semidirect |
| 60. C22×C79 | #376 | semidirect |
| 71. C2×C79 | C2×#376 | semidirect |
| 79. C79 | C22×#376 | semidirect |
| 135. C22 | #19098408 | direct (N × H) |
| 145. C2 | C2×#19098408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×Dic79 | 2 |
| C2×#19098408 | 2 |
| C22×C79⋊#95 | 2 |
| C22×#95×C79 | 2 |
| C22×#376 | 79 |