Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
690 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #23774327 | C2 | semidirect |
| 3. #23771756 | C2 | semidirect |
| 4. #23764227 | C2 | semidirect |
| 5. #23762082 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1545 | C2 | semidirect |
| 195. #1545 | D79 | semidirect |
| 197. C79 | #10281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774327 | 2 |
| #23774318 | 2 |
| #23771756 | 2 |
| #23764227 | 2 |
| #23762082 | 2 |
| #23761232 | 2 |
| C79×#1545 | 2 |
| #10281 | 79 |