Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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. #23761527 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 5. C79×#1394 | C2 | semidirect |
| 11. #19098546 | C4 | semidirect |
| 46. #14579080 | C2×C4 | semidirect |
| 54. #101×C79 | C2×C4 | semidirect |
| 194. #1394 | D79 | semidirect |
| 195. C79 | #12587 | semidirect |
| 242. #101 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098546 | 2 |
| #23765991 | 2 |
| #23761527 | 2 |
| #23761526 | 2 |
| C79×#1394 | 2 |
| #12587 | 79 |