Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
532 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C4×#14579080 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 5. C4×#101×C79 | C2 | semidirect |
| 18. #19098359 | C4 | direct (N × H) |
| 42. #14579080 | C2×C4 | semidirect |
| 60. #101×C79 | C2×C4 | semidirect |
| 176. C4×C79 | #355 | semidirect |
| 190. C4×#101 | D79 | semidirect |
| 192. C79 | C4×#355 | semidirect |
| 241. #101 | C4×D79 | semidirect |
| 366. C4 | #19098359 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579150 | 2 |
| C2×#19098359 | 2 |
| C4×#14579080 | 2 |
| #23761526 | 2 |
| C4×#101×C79 | 2 |
| C4×#355 | 79 |