Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×#19098995 | C2 | semidirect |
| 2. #23765709 | C2 | direct (N × H) |
| 3. C2×Dic1264 | C2 | semidirect |
| 4. C2×#19098402 | C2 | semidirect |
| 5. C2×D2528 | C2 | semidirect |
| 6. C22×C32×C79 | C2 | semidirect |
| 9. #19098995 | C22 | semidirect |
| 13. Dic1264 | C22 | semidirect |
| 14. #19098402 | C22 | semidirect |
| 15. D2528 | C22 | semidirect |
| 19. C2×C32×C79 | C22 | semidirect |
| 84. C2×C79 | #2262 | semidirect |
| 92. C22×C32 | D79 | semidirect |
| 93. C79 | C2×#2262 | semidirect |
| 106. C2×C32 | C2×D79 | semidirect |
| 171. C2 | #23765709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098995 | 2 |
| #23765709 | 2 |
| C2×Dic1264 | 2 |
| C2×#19098402 | 2 |
| C2×D2528 | 2 |
| C22×C32×C79 | 2 |
| C2×#2262 | 79 |