Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 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 |
|---|---|---|
| 3. #23771798 | C2 | semidirect |
| 5. #23762084 | C2 | semidirect |
| 6. #23762080 | C2 | semidirect |
| 7. C79×#1276 | C2 | semidirect |
| 112. C42×C79 | SD16 | semidirect |
| 181. #1276 | D79 | semidirect |
| 182. C79 | #10283 | semidirect |
| 287. C42 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774530 | 2 |
| #23774327 | 2 |
| #23771798 | 2 |
| #23764228 | 2 |
| #23762084 | 2 |
| #23762080 | 2 |
| C79×#1276 | 2 |
| #10283 | 79 |