Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19098610 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. C2×#19098344 | C2 | semidirect |
| 6. #23761498 | C2 | semidirect |
| 7. C79×#1383 | C2 | semidirect |
| 54. #14579097 | D4 | semidirect |
| 64. #108×C79 | D4 | semidirect |
| 185. #1383 | D79 | semidirect |
| 186. C79 | #13010 | semidirect |
| 242. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098817 | 2 |
| C2×#19098610 | 2 |
| C2×#19098377 | 2 |
| C2×#19098375 | 2 |
| C2×#19098344 | 2 |
| #23761498 | 2 |
| C79×#1383 | 2 |
| #13010 | 79 |