Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23765186 | C2 | semidirect |
| 5. #23761507 | C2 | semidirect |
| 6. #23761484 | C2 | semidirect |
| 7. C79×#1944 | C2 | semidirect |
| 20. #19098372 | C4 | semidirect |
| 48. #14579101 | C2×C4 | semidirect |
| 67. #106×C79 | C2×C4 | semidirect |
| 82. Dic316 | C4⋊C4 | semidirect |
| 86. D632 | C4⋊C4 | semidirect |
| 186. #1944 | D79 | semidirect |
| 189. C79 | #12943 | semidirect |
| 245. #106 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772202 | 2 |
| #23765186 | 2 |
| C2×#19098372 | 2 |
| #23765110 | 2 |
| #23761507 | 2 |
| #23761484 | 2 |
| C79×#1944 | 2 |
| #12943 | 79 |