Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 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. #23771988 | C2 | semidirect |
| 3. #23765116 | C2 | semidirect |
| 4. C2×#19098344 | C2 | semidirect |
| 5. #23761506 | C2 | semidirect |
| 6. #23761505 | C2 | semidirect |
| 7. C79×#2140 | C2 | semidirect |
| 13. #19098813 | C4 | semidirect |
| 49. #14579095 | D4 | semidirect |
| 53. #14579093 | C2×C4 | semidirect |
| 62. C2×D8×C79 | C2×C4 | semidirect |
| 68. #107×C79 | D4 | semidirect |
| 190. #2140 | D79 | semidirect |
| 194. C79 | #12999 | semidirect |
| 221. C2×D8 | C4×D79 | semidirect |
| 250. #107 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098813 | 2 |
| #23771988 | 2 |
| #23765116 | 2 |
| C2×#19098344 | 2 |
| #23761506 | 2 |
| #23761505 | 2 |
| C79×#2140 | 2 |
| #12999 | 79 |