Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19098850 | C2 | semidirect |
| 3. #23762543 | C2 | direct (N × H) |
| 4. C2×#19098312 | C2 | semidirect |
| 5. C2×#19098292 | C2 | semidirect |
| 6. C2×#494×C79 | C2 | semidirect |
| 15. #19098850 | C22 | semidirect |
| 19. #19098312 | C22 | semidirect |
| 20. #19098292 | C22 | semidirect |
| 25. #494×C79 | C22 | semidirect |
| 152. C2×C79 | #1634 | semidirect |
| 157. C2×#494 | D79 | semidirect |
| 162. C79 | C2×#1634 | semidirect |
| 174. #494 | C2×D79 | semidirect |
| 308. C2 | #23762543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099279 | 2 |
| C2×#19098850 | 2 |
| #23762543 | 2 |
| C2×#19098312 | 2 |
| C2×#19098292 | 2 |
| C2×#494×C79 | 2 |
| C2×#1634 | 79 |