Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
800 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23764378 | C2 | semidirect |
| 2. #23764229 | C2 | semidirect |
| 3. #23762138 | C2 | semidirect |
| 4. #23762135 | C2 | semidirect |
| 14. #562×C79 | C4 | semidirect |
| 147. C79 | #8532 | semidirect |
| 148. #562 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764378 | 2 |
| #23764229 | 2 |
| #23762138 | 2 |
| #23762135 | 2 |
| C79×#3548 | 2 |
| #8532 | 79 |